JMAP REGENTS AT RANDOM - Free resources for Algebra I ......Algebra II Regents Exam Questions at Random 3 10 Written in simplest form, the fraction x3 −9x 9−x2, where x ≠±3,

$Page 1: JMAP REGENTS AT RANDOM - Free resources for Algebra I ......Algebra II Regents Exam Questions at Random 3 10 Written in simplest form, the fraction x3 −9x 9−x2, where x ≠±3,$
JMAP REGENTS AT RANDOM

NY Algebra II Regents Exam Questions from Spring 2015 to January 2020 Sorted at Random

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Algebra II Regents Exam Questions at Randomwww.jmap.org

1

Algebra II Regents at Random

1 The resting blood pressure of an adult patient can be modeled by the function P below, where P(t) is the pressure in millimeters of mercury after time t in seconds.

P(t) = 24cos(3πt) + 120On the set of axes below, graph y = P(t) over the domain 0 ≤ t ≤ 2.

Determine the period of P. Explain what this value represents in the given context. Normal resting blood pressure for an adult is 120 over 80. This means that the blood pressure oscillates between a maximum of 120 and a minimum of 80. Adults with high blood pressure (above 140 over 90) and adults with low blood pressure (below 90 over 60) may be at risk for health disorders. Classify the given patient's blood pressure as low, normal, or high and explain your reasoning.

2 Which representation of a quadratic has imaginary roots?

1)2) 2(x + 3)2 = 64

3)4) 2x2 + 32 = 0

3 Suppose two sets of test scores have the same mean, but different standard deviations, σ1 and σ2 , with σ2 > σ1 . Which statement best describes the variability of these data sets?1) Data set one has the greater variability.2) Data set two has the greater variability.3) The variability will be the same for each data

set.4) No conclusion can be made regarding the

variability of either set.


2

4 Sodium iodide-131, used to treat certain medical conditions, has a half-life of 1.8 hours. The data table below shows the amount of sodium iodide-131, rounded to the nearest thousandth, as the dose fades over time.

Numberof

Half Lives1 2 3 4 5

Amount ofSodium

Iodide-131139.000 69.500 34.750 17.375 8.688

What approximate amount of sodium iodide-131 will remain in the body after 18 hours?1) 0.001 3) 0.2712) 0.136 4) 0.543

5 On average, college seniors graduating in 2012 could compute their growing student loan debt using the function D(t) = 29,400(1.068) t , where t is time in years. Which expression is equivalent to 29,400(1.068) t and could be used by students to identify an approximate daily interest rate on their loans?

1) 29,400 1.0681

365

t

2) 29,400 1.068365

365t

3) 29,400 1 + 0.068365

t

4) 29,400 1.0681

365

365t

6 The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18. Determine the number of students who scored between 200 and 245.

7 Which statement is true about the graph of

f(x) = 18

x

?

1) The graph is always increasing.2) The graph is always decreasing.3) The graph passes through (1,0).4) The graph has an asymptote, x = 0.

8 The roots of the equation 3x2 + 2x = −7 are

1) −2,−13

2) −73 ,1

3) −13 ±

2i 53

4) −13 ±

113

9 The expression 6 − (3x − 2i)2 is equivalent to1) −9x2 + 12xi + 102) 9x 2 − 12xi + 23) −9x 2 + 104) −9x2 + 12xi − 4i + 6


3

10 Written in simplest form, the fraction x3 − 9x9− x2 ,

where x ≠ ±3, is equivalent to1) −x2) x

3)−x(x + 3)(3 + x)

4)x(x − 3)(3 − x)

11 The Wells family is looking to purchase a home in a suburb of Rochester with a 30-year mortgage that has an annual interest rate of 3.6%. The house the family wants to purchase is $152,500 and they will make a $15,250 down payment and borrow the remainder. Use the formula below to determine their monthly payment, to the nearest dollar.

M =

P r12

1 + r12

n

1+ r12

n

− 1

M = monthly paymentP = amount borrowedr = annual interest rate

n = total number of monthly payments

12 The expression 2 − x − 1x + 2 is equivalent to

1) 1 − 3x + 2

2) 1 + 3x + 2

3) 1 − 1x + 2

4) 1 + 1x + 2

13 Write a recursive formula for the sequence 6,9,13.5,20.25,. . .

14 For all values of x for which the expression is

defined, x3 + 2x 2 − 9x − 18x 3 − x2 − 6x

, in simplest form, is

equivalent to1) 3

2) −172

3) x + 3x

4) x 2 − 9x(x − 3)

15 Consider the following patterns: I. 16,−12,9,−6.75,. . . II. 1,4,9,16,. . . III. 6,18,30,42,. . .

IV. 12 , 2

3 , 34 , 4

5 ,. . .

Which pattern is geometric?1) I2) II3) III4) IV

16 Tides are a periodic rise and fall of ocean water. On a typical day at a seaport, to predict the time of the next high tide, the most important value to have would be the1) time between consecutive low tides2) time when the tide height is 20 feet3) average depth of water over a 24-hour period4) difference between the water heights at low

and high tide


4

17 The table below gives air pressures in kPa at selected altitudes above sea level measured in kilometers.

x Altitude (km) 0 1 2 3 4 5y Air Pressure (kPa) 101 90 79 70 62 54

Write an exponential regression equation that models these data rounding all values to the nearest thousandth. Use this equation to algebraically determine the altitude, to the nearest hundredth of a kilometer, when the air pressure is 29 kPa.

18 There are 440 students at Thomas Paine High School enrolled in U.S. History. On the April report card, the students' grades are approximately normally distributed with a mean of 79 and a standard deviation of 7. Students who earn a grade less than or equal to 64.9 must attend summer school. The number of students who must attend summer school for U.S. History is closest to1) 32) 53) 104) 22

19 Rowan is training to run in a race. He runs 15 miles in the first week, and each week following, he runs 3% more than the week before. Using a geometric series formula, find the total number of miles Rowan runs over the first ten weeks of training, rounded to the nearest thousandth.

20 What is the solution set of the equation 2x − 3x

x + 3 = xx + 3 ?

1) {3}

2) 32

3) {−2,3}

4) −1, 32

21 Algebraically solve for x: −3x + 3 + 1

2 = x6 − 1

2

22 A student is chosen at random from the student body at a given high school. The probability that the student selects Math as the favorite subject is 14. The probability that the student chosen is a

junior is 116459. If the probability that the student

selected is a junior or that the student chooses Math

as the favorite subject is 47108, what is the exact

probability that the student selected is a junior whose favorite subject is Math? Are the events "the student is a junior" and "the student's favorite subject is Math" independent of each other? Explain your answer.

23 The recursive formula to describe a sequence is shown below.

a 1 = 3

an = 1+ 2an − 1

State the first four terms of this sequence. Can this sequence be represented using an explicit geometric formula? Justify your answer.


5

24 Point M t, 47

is located in the second quadrant on

the unit circle. Determine the exact value of t.

25 Express the fraction 2x32

16x4

14

in simplest radical

form.

26 Elizabeth tried to find the product of (2 + 4i) and (3 − i), and her work is shown below.

(2+ 4i)(3 − i)

= 6 − 2i + 12i − 4i2

= 6 + 10i − 4i2

= 6 + 10i − 4(1)

= 6 + 10i − 4

= 2 + 10iIdentify the error in the process shown and determine the correct product of (2 + 4i) and (3 − i).

27 Which expression can be rewritten as (x + 7)(x − 1)?1) (x + 3)2 − 162) (x + 3)2 − 10(x + 3) − 2(x + 3) + 20

3)(x − 1)(x2 − 6x − 7)

(x + 1)

4)(x + 7)(x2 + 4x + 3)

(x + 3)

28 A savings account, S, has an initial value of $50. The account grows at a 2% interest rate compounded n times per year, t, according to the function below.

S(t) = 50 1 + .02n

nt

Which statement about the account is correct?1) As the value of n increases, the amount of

interest per year decreases.2) As the value of n increases, the value of the

account approaches the function S(t) = 50e0.02t .3) As the value of n decreases to one, the amount

of interest per year increases.4) As the value of n decreases to one, the value of

the account approaches the function S(t) = 50(1− 0.02) t .

29 Sonja is cutting wire to construct a mobile. She cuts 100 inches for the first piece, 80 inches for the second piece, and 64 inches for the third piece. Assuming this pattern continues, write an explicit equation for a n , the length in inches of the nth piece. Sonja only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern. Will she have enough wire? Justify your answer.

30 If cosθ = −34 and θ is in Quadrant III, then sinθ is

equivalent to

1) −7

4

2)7

4

3) −54

4) 54


6

31 Joseph was curious to determine if scent improves memory. A test was created where better memory is indicated by higher test scores. A controlled experiment was performed where one group was given the test on scented paper and the other group was given the test on unscented paper. The summary statistics from the experiment are given below.

Scented Paper Unscented Paperx 23 18sx 2.898 2.408

Calculate the difference in means in the experimental test grades (scented -unscented). A simulation was conducted in which the subjects' scores were rerandomized into two groups 1000 times. The differences of the group means were calculated each time. The results are shown below.

Use the simulation results to determine the interval representing the middle 95% of the difference in means, to the nearest hundredth. Is the difference in means in Joseph's experiment statistically significant based on the simulation? Explain.


7

32 The populations of two small towns at the beginning of 2018 and their annual population growth rate are shown in the table below.

Town Population Annual PopulationGrowth Rate

Jonesville 1240 6% increaseWilliamstown 890 11% increase

Assuming the trend continues, approximately how many years after the beginning of 2018 will it take for the populations to be equal?1) 7 3) 682) 20 4) 125

33 The graph of y = f(x) is shown below. The function has a leading coefficient of 1.

Write an equation for f(x). The function g is formed by translating function f left 2 units. Write an equation for g(x).

34 When the function p(x) is divided by x − 1 the

quotient is x2 + 7 + 5x − 1 . State p(x) in standard

form.

35 Where i is the imaginary unit, the expression (x + 3i)2 − (2x − 3i)2 is equivalent to1) −3x 2

2) −3x 2 − 183) −3x2 + 18xi4) −3x2 − 6xi − 18

36 Stephanie found that the number of white-winged cross bills in an area can be represented by the formula C = 550(1.08) t , where t represents the number of years since 2010. Which equation correctly represents the number of white-winged cross bills in terms of the monthly rate of population growth?1) C = 550(1.00643) t

2) C = 550(1.00643)12t

3) C = 550(1.00643)t

12

4) C = 550(1.00643) t + 12

37 Determine, to the nearest tenth of a year, how long

it would take an investment to double at a 3 34 %

interest rate, compounded continuously.


8

38 Mary bought a pack of candy. The manufacturer claims that 30% of the candies manufactured are red. In her pack, 14 of the 60 candies are red. She ran a simulation of 300 samples, assuming the manufacturer is correct. The results are shown below.

Based on the simulation, determine the middle 95% of plausible values that the proportion of red candies in a pack is within. Based on the simulation, is it unusual that Mary’s pack had 14 red candies out of a total of 60? Explain.

39 The height above ground for a person riding a Ferris wheel after t seconds is modeled by

h(t) = 150sin π45 t + 67.5

+ 160 feet. How many

seconds does it take to go from the bottom of the wheel to the top of the wheel?1) 102) 453) 904) 150

40 If f(x) = log3x and g(x) is the image of f(x) after a translation five units to the left, which equation represents g(x)?1) g(x) = log3(x + 5)2) g(x) = log3 x + 53) g(x) = log3(x − 5)4) g(x) = log3 x − 5

41 What is the inverse of f(x) = x3 − 2?1) f −1 (x) = x3 + 22) f −1 (x) = ± x3 + 23) f −1 (x) = x + 23

4) f −1 (x) = ± x + 23

42 If p(x) = 2ln(x) − 1 and m(x) = ln(x + 6), then what is the solution for p(x) = m(x)?1) 1.652) 3.143) 5.624) no solution

43 Solve algebraically for all values of x: 6− 2x + x = 2(x + 15) − 9


9

44 A group of students was trying to determine the proportion of candies in a bag that are blue. The company claims that 24% of candies in bags are blue. A simulation was run 100 times with a sample size of 50, based on the premise that 24% of the candies are blue. The approximately normal results of the simulation are shown in the dot plot below.

The simulation results in a mean of 0.254 and a standard deviation of 0.060. Based on this simulation, what is a plausible interval containing the middle 95% of the data?1) (0.194,0.314) 3) (−0.448,0.568)2) (0.134,0.374) 4) (0.254,0.374)

45 The results of simulating tossing a coin 10 times, recording the number of heads, and repeating this 50 times are shown in the graph below.

Based on the results of the simulation, which statement is false?1) Five heads occurred most often, which is

consistent with the theoretical probability of obtaining a heads.

2) Eight heads is unusual, as it falls outside the middle 95% of the data.

3) Obtaining three heads or fewer occurred 28% of the time.

4) Seven heads is not unusual, as it falls within the middle 95% of the data.

46 A veterinary pharmaceutical company plans to test a new drug to treat a common intestinal infection among puppies. The puppies are randomly assigned to two equal groups. Half of the puppies will receive the drug, and the other half will receive a placebo. The veterinarians monitor the puppies. This is an example of which study method?1) census2) observational study3) survey4) controlled experiment

47 What are the solution(s) to the system of equations shown below?

x2 + y2 = 5

y = 2x1) x = 1 and x = −12) x = 13) (1,2) and (−1,−2)4) (1,2), only


10

48 Solve the equation 2x 2 + 5x + 8 = 0. Express the answer in a + bi form.

49 What is the inverse of f(x) = −6(x − 2)?

1) f −1 (x) = −2− x6

2) f −1 (x) = 2 − x6

3) f −l (x) = 1−6(x − 2)

4) f −1 (x) = 6(x + 2)

50 Given cosθ = 725, where θ is an angle in standard

position terminating in quadrant IV, and sin2θ + cos2θ = 1, what is the value of tanθ ?

1) −2425

2) −247

3) 2425

4) 247

51 The terminal side of θ , an angle in standard

position, intersects the unit circle at P −13 ,−

83

.

What is the value of sec θ?1) −3

2) −3 8

8

3) −13

4) −8

3

52 The profit function, p(x), for a company is the cost function, c(x), subtracted from the revenue function, r(x). The profit function for the Acme Corporation is p(x) = −0.5x2 + 250x − 300 and the revenue function is r(x) = −0.3x 2 + 150x. The cost function for the Acme Corporation is1) c(x) = 0.2x 2 − 100x + 3002) c(x) = 0.2x 2 + 100x + 3003) c(x) = −0.2x2 + 100x − 3004) c(x) = −0.8x2 + 400x − 300

53 Which function is even?1) f(x) = sinx2) f(x) = x2 − 43) f(x) = x − 2| | + 54) f(x) = x4 + 3x3 + 4

54 Julia deposits $2000 into a savings account that earns 4% interest per year. The exponential function that models this savings account is y = 2000(1.04) t , where t is the time in years. Which equation correctly represents the amount of money in her savings account in terms of the monthly growth rate?1) y = 166.67(1.04)0.12t

2) y = 2000(1.01) t

3) y = 2000(1.0032737)12t

4) y = 166.67(1.0032737) t

55 Explain why 8134 equals 27.


11

56 A runner is using a nine-week training app to prepare for a "fun run." The table below represents the amount of the program completed, A, and the distance covered in a session, D, in miles.

A 49

59

69

89 1

D 2 2 2.25 3 3.25

Based on these data, write an exponential regression equation, rounded to the nearest thousandth, to model the distance the runner is able to complete in a session as she continues through the nine-week program.

57 A fast-food restaurant analyzes data to better serve its customers. After its analysis, it discovers that the events D, that a customer uses the drive-thru, and F, that a customer orders French fries, are independent. The following data are given in a report:

P(F) = 0.8

P(F∩D) = 0.456

Given this information, P(F | D) is1) 0.3442) 0.36483) 0.574) 0.8

58 The hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y = 3.06sin(0.017x − 1.40) + 12.23. How many hours of daylight, to the nearest tenth, does this model predict for February 14, 2013?1) 9.42) 10.43) 12.14) 12.2

59 Given tanθ = 724 , and θ terminates in Quadrant III,

determine the value of cosθ .

60 A random sample of 100 people that would best estimate the proportion of all registered voters in a district who support improvements to the high school football field should be drawn from registered voters in the district at a1) football game2) supermarket3) school fund-raiser4) high school band concert

61 If f(x) = x 2 + 9 and g(x) = x + 3, which operation would not result in a polynomial expression?1) f(x) + g(x)2) f(x) − g(x)3) f(x) •g(x)4) f(x) ÷ g(x)

62 The graph of y = log2x is translated to the right 1 unit and down 1 unit. The coordinates of the x-intercept of the translated graph are 1) (0,0)2) (1,0)3) (2,0)4) (3,0)


12

63 Jake wants to buy a car and hopes to save at least $5000 for a down payment. The table below summarizes the amount of money he plans to save each week.

Week 1 2 3 4 5Money Saved, in Dollars 2 5 12.5 31.25 ...

Based on this plan, which expression should he use to determine how much he has saved in n weeks?

1)2− 2(2.5n)

1− 2.5 3) 1− 2.5n

1 − 2.5

2)2− 2(2.5n − 1 )

1 − 2.5 4) 1− 2.5n − 1

1 − 2.5

64 Camryn puts $400 into a savings account that earns 6% annually. The amount in her account can be modeled by C(t) = 400(1.06) t where t is the time in years. Which expression best approximates the amount of money in her account using a weekly growth rate?1) 400(1.001153846) t

2) 400(1.001121184) t

3) 400(1.001153846)52t

4) 400(1.001121184)52t

65 For positive values of x, which expression is

equivalent to 16x2 • x23 + 8x53

1) 6 x35

2) 6 x53

3) 4 x23 + 2 x53

4) 4 x3 + 2 x35

66 Explain what a rational exponent, such as 52 means.

Use this explanation to evaluate 952 .

67 The first term of a geometric sequence is 8 and the fourth term is 216. What is the sum of the first 12 terms of the corresponding series?1) 236,1922) 708,5843) 2,125,7604) 6,377,288

68 Which equation represents a parabola with a focus of (−2,5) and a directrix of y = 9?1) (y − 7)2 = 8(x + 2)2) (y − 7)2 = −8(x + 2)3) (x + 2)2 = 8(y − 7)4) (x + 2)2 = −8(y − 7)

69 What is the quotient when 10x3 − 3x2 − 7x + 3 is divided by 2x − 1?1) 5x2 + x + 32) 5x2 − x + 33) 5x2 − x − 34) 5x2 + x − 3


13

70 Selected values for the functions f and g are shown in the tables below.

x f(x) x g(x)−3.12 −4.88 −2.01 −1.01

0 −6 0 0.581.23 −4.77 8.52 2.538.52 2.53 13.11 3.019.01 3.01 16.52 3.29

A solution to the equation f(x) = g(x) is1) 0 3) 3.012) 2.53 4) 8.52

71 The function f(x) = a cos bx + c is plotted on the graph shown below.

What are the values of a, b, and c?1) a = 2, b = 6, c = 32) a = 2, b = 3, c = 13) a = 4, b = 6, c = 5

4) a = 4, b = π3 , c = 3

72 Evaluate j(−1) given j(x) = 2x4 − x 3 − 35x 2 + 16x + 48. Explain what your answer tells you about x + 1 as a factor. Algebraically find the remaining zeros of j(x).

73 Which expression is equivalent to (2x − i)2 − (2x − i)(2x + 3i) where i is the imaginary unit and x is a real number?1) −4 − 8xi2) −4 − 4xi3) 24) 8x − 4i

74 Factor completely over the set of integers: 16x 4 − 81. Sara graphed the polynomial y = 16x4 − 81 and stated “All the roots of y = 16x4 − 81 are real.” Is Sara correct? Explain your reasoning.

75 Given f(x) = 12 x + 8, which equation represents the

inverse, g(x)?1) g(x) = 2x − 82) g(x) = 2x − 16

3) g(x) = −12 x + 8

4) g(x) = −12 x − 16


14

76 If f(x) = ax where a > 1, then the inverse of the function is1) f −1 (x) = logx a2) f −1 (x) = a logx3) f −1 (x) = loga x4) f −1 (x) = x loga

77 Which statement(s) are true for all real numbers?I (x − y)2 = x2 + y2

II (x + y)3 = x3 + 3xy + y 3

1) I, only2) II, only3) I and II4) neither I nor II

78 If n = a 5 and m = a, where a > 0, an expression

for nm could be

1) a52

2) a 4

3) a 23

4) a 3

79 When a ball bounces, the heights of consecutive bounces form a geometric sequence. The height of the first bounce is 121 centimeters and the height of the third bounce is 64 centimeters. To the nearest centimeter, what is the height of the fifth bounce?1) 252) 343) 364) 42

80 The expression (x + a)(x + b) can not be written as1) a(x + b) + x(x + b)2) x2 + abx + ab3) x2 + (a + b)x + ab4) x(x + a) + b(x + a)

81 Irma initially ran one mile in over ten minutes. She then began a training program to reduce her one-mile time. She recorded her one-mile time once a week for twelve consecutive weeks, as modeled in the graph below.

Which statement regarding Irma’s one-mile training program is correct?1) Her one-mile speed increased as the number of

weeks increased.2) Her one-mile speed decreased as the number of

weeks increased.3) If the trend continues, she will run under a

six-minute mile by week thirteen.4) She reduced her one-mile time the most

between weeks ten and twelve.

82 Determine the quotient and remainder when (6a 3 + 11a 2 − 4a − 9) is divided by (3a − 2).

Express your answer in the form q(a) +r(a)d(a) .


15

83 On the grid below, graph the function y = log2(x − 3) + 1

84 For x > 0, which expression is equivalent to

x23 • x5

x6 ?

1) x

2) x32

3) x3

4) x10

85 The solution set for the equation b = 2b 2 − 64 is1) {−8}2) {8}3) {±8}4) { }

86 A study of black bears in the Adirondacks reveals that their population can be represented by the function P(t) = 3500(1.025) t , where t is the number of years since the study began. Which function is correctly rewritten to reveal the monthly growth rate of the black bear population?1) P(t) = 3500(1.00206)12t

2) P(t) = 3500(1.00206)t

12

3) P(t) = 3500(1.34489)12t

4) P(t) = 3500(1.34489)t

12

87 Given: f(x) = 2x2 + x − 3 and g(x) = x − 1Express f(x) •g(x) − [f(x) + g(x)] as a polynomial in standard form.


16

88 The function below models the average price of gas in a small town since January 1st.G(t) = −0.0049t4 + 0.0923t3 − 0.56t2 + 1.166t + 3.23, where 0 ≤ t ≤ 10.If G(t) is the average price of gas in dollars and t represents the number of months since January 1st, the absolute maximum G(t) reaches over the given domain is about1) $1.602) $3.923) $4.014) $7.73

89 On the grid below, graph the function f(x) = x3 − 6x2 + 9x + 6 on the domain −1 ≤ x ≤ 4.

90 The value(s) of x that satisfy

x2 − 4x − 5 = 2x − 10 are1) {5}2) {7}3) {5,7}4) {3,5,7}

91 The average depreciation rate of a new boat is approximately 8% per year. If a new boat is purchased at a price of $75,000, which model is a recursive formula representing the value of the boat n years after it was purchased?1) an = 75,000(0.08)n

2) a 0 = 75,000

an = (0.92)n

3) an = 75,000(1.08)n

4) a 0 = 75,000

an = 0.92(an − 1 )

92 The equation t = 10.0105 ln A

5000

relates time, t,

in years, to the amount of money, A, earned by a $5000 investment. Which statement accurately describes the relationship between the average rates of change of t on the intervals [6000, 8000] and [9000, 12,000]?1) A comparison cannot be made because the

intervals are different sizes.2) The average rate of change is equal for both

intervals.3) The average rate of change is larger for the

interval [6000, 8000].4) The average rate of change is larger for the

interval [9000, 12,000].

93 The average monthly high temperature in Buffalo, in degrees Fahrenheit, can be modeled by the function B(t) = 25.29sin(0.4895t − 1.9752) + 55.2877, where t is the month number (January = 1). State, to the nearest tenth, the average monthly rate of temperature change between August and November. Explain its meaning in the given context.


17

94 Website popularity ratings are often determined using models that incorporate the number of visits per week a website receives. One model for ranking websites is P(x) = log(x − 4), where x is the number of visits per week in thousands and P(x) is the website's popularity rating. According to this model, if a website is visited 16,000 times in one week, what is its popularity rating, rounded to the nearest tenth? Graph y = P(x) on the axes below.

An alternative rating model is represented by R(x) = 12 x − 6, where x is the number of visits per week in

thousands. Graph R(x) on the same set of axes. For what number of weekly visits will the two models provide the same rating?

95 Which expression(s) are equivalent to x2 − 4x2x ,

where x ≠ 0?

I. x2 − 2 II. x − 4

2 III. x − 12 − 3

21) II, only2) I and II3) II and III4) I, II, and III

96 If p(x) = 2x3 − 3x + 5, what is the remainder of p(x) ÷ (x − 5)?1) −2302) 03) 404) 240


18

97 There are 400 students in the senior class at Oak Creek High School. All of these students took the SAT. The distribution of their SAT scores is approximately normal. The number of students who scored within 2 standard deviations of the mean is approximately1) 752) 953) 3004) 380

98 Consider f(x) = 4x2 + 6x − 3, and p(x) defined by the graph below.

The difference between the values of the maximum of p and minimum of f is1) 0.252) 1.253) 3.254) 10.25

99 If A = −3+ 5i, B = 4− 2i, and C = 1+ 6i, where i is the imaginary unit, then A − BC equals1) 5 − 17i2) 5 + 27i3) −19 − 17i4) −19 + 27i

100 If x − 1 is a factor of x3 − kx 2 + 2x , what is the value of k?1) 02) 23) 34) −3

101 Given c(m) = m3 − 2m2 + 4m− 8, the solution of c(m) = 0 is1) ±22) 2, only3) 2i,24) ±2i,2

102 The function N(t) = 100e−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?1) [1,10]2) [10,20]3) [15,25]4) [1,30]

103 If f(x) is an even function, which function must also be even?1) f(x − 2)2) f(x) + 33) f(x + 1)4) f(x + 1) + 3

104 If the function g(x) = ab x represents exponential growth, which statement about g(x) is false?1) a > 0 and b > 12) The y-intercept is (0,a).3) The asymptote is y = 0.4) The x-intercept is (b,0).


19

105 Graph the following function on the axes below.f(x) = log3(2 − x)

State the domain of f. State the equation of the asymptote.

106 Given y > 0, the expression 3x2y • 27x3y 23 is equivalent to1) 81x5y 3

2) 31.5 x2y

3) 352 x 2 y

53

4) 332 x 2 y

76

107 Algebraically solve the following system of equations.

(x − 2)2 + (y − 3)2 = 16

x + y − 1 = 0

108 Write −12 i3 −9 − 4

− 3i2 in simplest a + bi

form.

109 Savannah just got contact lenses. Her doctor said she can wear them 2 hours the first day, and can then increase the length of time by 30 minutes each day. If this pattern continues, which formula would not be appropriate to determine the length of time, in either minutes or hours, she could wear her contact lenses on the nth day?1) a 1 = 120

an = an − 1 + 302) an = 90 + 30n3) a 1 = 2

an = an − 1 + 0.54) an = 2.5+ 0.5n

110 A sketch of r(x) is shown below.

An equation for r(x) could be1) r(x) = (x − a)(x + b)(x + c)2) r(x) = (x + a)(x − b)(x − c)2

3) r(x) = (x + a)(x − b)(x − c)4) r(x) = (x − a)(x + b)(x + c)2


20

111 What is the solution set for x in the equation below?

x + 1 − 1 = x1) {1}2) {0}3) {−1,0}4) {0,1}

112 Completely factor the following expression: x2 + 3xy + 3x3 + y

113 The scores on a mathematics college-entry exam are normally distributed with a mean of 68 and standard deviation 7.2. Students scoring higher than one standard deviation above the mean will not be enrolled in the mathematics tutoring program. How many of the 750 incoming students can be expected to be enrolled in the tutoring program?1) 6312) 5123) 2384) 119

114 Algebraically solve for x: 72x − 2

x + 1 = 14

115 What is the inverse of the function y = 4x + 5?

1) x = 14 y − 5

4

2) y = 14 x − 5

43) y = 4x − 5

4) y = 14x + 5

116 What is the inverse of f(x) = xx + 2 , where x ≠ −2?

1) f − 1 (x) = 2xx − 1

2) f − 1 (x) = −2xx − 1

3) f − 1 (x) = xx − 2

4) f − 1 (x) = −xx − 2

117 The graph of y = f(x) is shown below.

Which expression defines f(x)?1) 2x2) 5(2x )

3) 5(2x2 )

4) 5(22x)

118 A person’s lung capacity can be modeled by the

function C(t) = 250sin 2π5 t

+ 2450, where C(t)

represents the volume in mL present in the lungs after t seconds. State the maximum value of this function over one full cycle, and explain what this value represents.


21

119 To determine if the type of music played while taking a quiz has a relationship to results, 16 students were randomly assigned to either a room softly playing classical music or a room softly playing rap music. The results on the quiz were as follows:

Classical: 74, 83, 77, 77, 84, 82, 90, 89 Rap: 77, 80, 78, 74, 69, 72, 78, 69

John correctly rounded the difference of the means of his experimental groups as 7. How did John obtain this value and what does it represent in the given context? Justify your answer. To determine if there is any significance in this value, John rerandomized the 16 scores into two groups of 8, calculated the difference of the means, and simulated this process 250 times as shown below.

Does the simulation support the theory that there may be a significant difference in quiz scores? Explain.

120 Justify why x 2 y 53

x 3 y 44 is equivalent to x

−112 y

23 using

properties of rational exponents, where x ≠ 0 and y ≠ 0.

121 If a 3 + 27

= (a + 3) a 2 +ma + 9

, then m equals

1) −92) −33) 34) 6


22

122 Determine an equation for the parabola with focus (4,−1) and directrix y = −5. (Use of the grid below is optional.)

123 The height, h(t) in cm, of a piston, is given by the

equation h(t) = 12cos π3 t

+ 8, where t represents

the number of seconds since the measurements began. Determine the average rate of change, in cm/sec, of the piston's height on the interval 1 ≤ t ≤ 2. At what value(s) of t, to the nearest tenth of a second, does h(t) = 0 in the interval 1 ≤ t ≤ 5? Justify your answer.

124 Evan graphed a cubic function, f(x) = ax 3 + bx 2 + cx + d , and determined the roots of f(x) to be ±1 and 2. What is the value of b, if a = 1?1) 12) 23) −14) −2

125 Determine for which polynomial(s) (x + 2) is a factor. Explain your answer.

P(x) = x4 − 3x3 − 16x − 12

Q(x) = x3 − 3x2 − 16x − 12

126 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a fifteen-year period. The company represents its revenue and costs as a function of time, in years, x, using the given functions.

R(x) = 550x3 − 12,000x2 + 83,000x + 7000C(x) = 880x3 − 21,000x2 + 150,000x − 160,000

The company's profits can be represented as the difference between its revenue and costs. Write the profit function, P(x), as a polynomial in standard form. Graph y = P(x) on the set of axes below over the domain 2 ≤ x ≤ 16.

Over the given domain, state when the company was the least profitable and the most profitable, to the nearest year. Explain how you determined your answer.


23

127 Consider the data in the table below.

Right Handed Left HandedMale 87 13

Female 89 11

What is the probability that a randomly selected person is male given the person is left handed?

1) 13200 3) 13

50

2) 13100 4) 13

24

128 Some smart-phone applications contain "in-app" purchases, which allow users to purchase special content within the application. A random sample of 140 users found that 35 percent made in-app purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the samples make in-app purchases. The approximately normal results are shown below.

Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth, for the simulated results. In the given context, explain what this value represents.


24

129 Given a(x) = x 4 + 2x 3 + 4x − 10 and b(x) = x + 2,

determine a(x)b(x) in the form q(x) +

r(x)b(x) . Is b(x) a

factor of a(x)? Explain.

130 Given P(x) = x3 − 3x2 − 2x + 4, which statement is true?1) (x − 1) is a factor because P(−1) = 2.2) (x + 1) is a factor because P(−1) = 2.3) (x + 1) is a factor because P(1) = 0.4) (x − 1) is a factor because P(1) = 0.

131 Data for the students enrolled in a local high school are shown in the Venn diagram below.

If a student from the high school is selected at random, what is the probability that the student is a sophomore given that the student is enrolled in Algebra II?

1) 85210

2) 85295

3) 85405

4) 851600

132 Researchers in a local area found that the population of rabbits with an initial population of 20 grew continuously at the rate of 5% per month. The fox population had an initial value of 30 and grew continuously at the rate of 3% per month. Find, to the nearest tenth of a month, how long it takes for these populations to be equal.

133 Chet has $1200 invested in a bank account modeled by the function P(n) = 1200(1.002)n , where P(n) is the value of his account, in dollars, after n months. Chet's debt is modeled by the function Q(n) = 100n, where Q(n) is the value of debt, in dollars, after n months. After n months, which function represents Chet's net worth, R(n)?1) R(n) = 1200(1.002)n + 100n2) R(n) = 1200(1.002)12n + 100n3) R(n) = 1200(1.002)n − 100n4) R(n) = 1200(1.002)12n − 100n

134 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be modeled by the function p(t) = 2560e0.017185t , where t is time in years after 1950 and p(t) is the population in millions. Determine the average rate of change of p(t) in millions of people per year, from 4 ≤ t ≤ 8. Round your answer to the nearest hundredth.

135 For the system shown below, what is the value of z?

y = −2x + 14

3x − 4z = 2

3x − y = 161) 52) 23) 64) 4


25

136 The table below shows the number of hours of daylight on the first day of each month in Rochester, NY.

Month Hours of DaylightJan. 9.4Feb. 10.6

March 11.9April 13.9May 14.7June 15.4July 15.1Aug. 13.9Sept. 12.5Oct. 11.1Nov. 9.7Dec. 9.0

Given the data, what is the average rate of change in hours of daylight per month from January 1st to April 1st? Interpret what this means in the context of the problem.

137 What is the solution set of the equation 2

3x + 1 = 1x − 6x

3x + 1?

1) −13 , 1

2

2) −13

3) 12

4) 13 ,−2

138 Solve the following system of equations algebraically for all values of a, b, and c.

a + 4b + 6c = 23

a + 2b + c = 2

6b + 2c = a + 14

139 A certain pain reliever is taken in 220 mg dosages and has a half-life of 12 hours. The function

A = 220 12

t12

can be used to model this situation,

where A is the amount of pain reliever in milligrams remaining in the body after t hours. According to this function, which statement is true?1) Every hour, the amount of pain reliever

remaining is cut in half.2) In 12 hours, there is no pain reliever remaining

in the body.3) In 24 hours, there is no pain reliever remaining

in the body.4) In 12 hours, 110 mg of pain reliever is

remaining.

140 An angle, θ , is in standard position and its terminal side passes through the point (2,−1). Find the exact value of sinθ .


26

141 Which function's graph has a period of 8 and reaches a maximum height of 1 if at least one full period is graphed?

1) y = −4cos π4 x

− 3

2) y = −4cos π4 x

+ 5

3) y = −4cos(8x) − 34) y = −4cos(8x) + 5

142 Which description could represent the graph of f(x) = 4x2 (x + a) − x − a , if a is an integer?1) As x → −∞, f(x) → ∞ , as x → ∞, f(x) → ∞ ,

and the graph has 3 x-intercepts.2) As x → −∞, f(x) → −∞ , as x → ∞, f(x) → ∞ ,

and the graph has 3 x-intercepts.3) As x → −∞, f(x) → ∞ , as x → ∞, f(x) → −∞ ,

and the graph has 4 x-intercepts.4) As x → −∞, f(x) → −∞ , as x → ∞, f(x) → ∞ ,

and the graph has 4 x-intercepts.

143 Brian deposited 1 cent into an empty non-interest bearing bank account on the first day of the month. He then additionally deposited 3 cents on the second day, 9 cents on the third day, and 27 cents on the fourth day. What would be the total amount of money in the account at the end of the 20th day if the pattern continued?1) $11,622,614.672) $17,433,922.003) $116,226,146.804) $1,743,392,200.00

144 If $5000 is put into a savings account that pays 3.5% interest compounded monthly, how much money, to the nearest ten cents, would be in that account after 6 years, assuming no money was added or withdrawn?1) $5177.802) $5941.303) $6146.304) $6166.50

145 The graph below represents national and New York State average gas prices.

If New York State's gas prices are modeled by G(x) and C > 0, which expression best approximates the national average x months from August 2014?1) G(x +C)2) G(x) +C3) G(x −C)4) G(x) −C


27

146 A survey about television-viewing preferences was given to randomly selected freshmen and seniors at Fairport High School. The results are shown in the table below.

Favorite Type of ProgramSports Reality Show Comedy Series

Senior 83 110 67Freshmen 119 103 54

A student response is selected at random from the results. State the exact probability the student response is from a freshman, given the student prefers to watch reality shows on television.

147 Which situation could be modeled using a geometric sequence?1) A cell phone company charges $30.00 per

month for 2 gigabytes of data and $12.50 for each additional gigabyte of data.

2) The temperature in your car is 79°. You lower the temperature of your air conditioning by 2° every 3 minutes in order to find a comfortable temperature.

3) David’s parents have set a limit of 50 minutes per week that he may play online games during the school year. However, they will increase his time by 5% per week for the next ten weeks.

4) Sarah has $100.00 in her piggy bank and saves an additional $15.00 each week.

148 3Written in simplest form, c2 − d 2

d 2 + cd − 2c2 where

c ≠ d , is equivalent to

1) c + dd + 2c

2) c − dd + 2c

3) −c − dd + 2c

4) −c + dd + 2c

149 A formula for work problems involving two people is shown below.

1t1+ 1

t2= 1

tb

t1 = the time taken by the first person to complete the job t2 = the time taken by the second person to complete the job tb = the time it takes for them working together to complete the job Fred and Barney are carpenters who build the same model desk. It takes Fred eight hours to build the desk while it only takes Barney six hours. Write an equation that can be used to find the time it would take both carpenters working together to build a desk. Determine, to the nearest tenth of an hour, how long it would take Fred and Barney working together to build a desk.

150 What is the solution set of x = 3x + 40 ?1) {−5,8}2) {8}3) {−4,10}4) { }


28

151 Consider the probability statements regarding events A and B below. P(A or B) = 0.3; P(A and B) = 0.2; and P(A| B) = 0.8What is P(B)?1) 0.12) 0.253) 0.3754) 0.667

152 The solutions to x + 3 − 4x − 1 = 5 are

1) 32 ±

172

2) 32 ±

172 i

3) 32 ±

332

4) 32 ±

332 i

153 The solutions to the equation 5x2 − 2x + 13 = 9 are

1) 15 ±

215

2) 15 ±

195 i

3) 15 ±

665 i

4) 15 ±

665

154 How many solutions exist for 1

1− x 2 = − 3x − 2| | + 5?

1) 12) 23) 34) 4

155 The Fahrenheit temperature, F(t), of a heated object at time t, in minutes, can be modeled by the function below. Fs is the surrounding temperature, F0 is the initial temperature of the object, and k is a constant.

F(t) = Fs + (F0 − Fs)e−kt

Coffee at a temperature of 195°F is poured into a container. The room temperature is kept at a constant 68°F and k = 0.05. Coffee is safe to drink when its temperature is, at most, 120°F. To the nearest minute, how long will it take until the coffee is safe to drink?1) 72) 103) 114) 18

156 The parabola described by the equation

y = 112 (x − 2)2 + 2 has the directrix at y = −1. The

focus of the parabola is1) (2,−1)2) (2,2)3) (2,3)4) (2,5)

157 Solve the following system of equations algebraically. x2 + y2 = 400

y = x − 28


29

158 A radio station claims to its advertisers that the mean number of minutes commuters listen to the station is 30. The station conducted a survey of 500 of their listeners who commute. The sample statistics are shown below.

x 29.11s x 20.718

A simulation was run 1000 times based upon the results of the survey. The results of the simulation appear below.

Based on the simulation results, is the claim that commuters listen to the station on average 30 minutes plausible? Explain your response including an interval containing the middle 95% of the data, rounded to the nearest hundredth.

159 A researcher randomly divides 50 bean plants into two groups. He puts one group by a window to receive natural light and the second group under artificial light. He records the growth of the plants weekly. Which data collection method is described in this situation?1) observational study2) controlled experiment3) survey4) systematic sample

160 Kenzie believes that for x ≥ 0, the expression

x27

x 35

is equivalent to x635 . Is she

correct? Justify your response algebraically.

161 A sociologist reviews randomly selected surveillance videos from a public park over a period of several years and records the amount of time people spent on a smartphone. The statistical procedure the sociologist used is called1) a census2) an experiment3) an observational study4) a sample survey


30

162 A number, minus twenty times its reciprocal, equals eight. The number is1) 10 or −22) 10 or 23) −10 or −24) −10 or 2

163 If aebt = c, where a, b, and c are positive, then t equals

1) ln cab

2) ln cba

3)ln c

a

b

4)ln c

a

lnb

164 Given the following polynomials x = (a + b + c)2

y = a 2 + b 2 + c2

z = ab + bc + ac Which identity is true?1) x = y − z2) x = y + z3) x = y − 2z4) x = y + 2z

165 The graphs of the equations y = x2 + 4x − 1 and y + 3 = x are drawn on the same set of axes. One solution of this system is1) (−5,−2)2) (−1,−4)3) (1,4)4) (−2,−1)

166 Carla wants to start a college fund for her daughter Lila. She puts $63,000 into an account that grows at a rate of 2.55% per year, compounded monthly. Write a function, C(t), that represents the amount of money in the account t years after the account is opened, given that no more money is deposited into or withdrawn from the account. Calculate algebraically the number of years it will take for the account to reach $100,000, to the nearest hundredth of a year.

167 The zeros of a quartic polynomial function h are −1, ±2, and 3. Sketch a graph of y = h(x) on the grid below.


31

168 Which expression is equivalent to 2x4 + 8x3 − 25x2 − 6x + 14

x + 6 ?

1) 2x3 + 4x 2 + x − 12+ 86x + 6

2) 2x 3 − 4x 2 − x + 14

3) 2x3 − 4x2 − x + 14x + 6

4) 2x 3 − 4x 2 − x

169 Griffin is riding his bike down the street in Churchville, N.Y. at a constant speed, when a nail gets caught in one of his tires. The height of the nail above the ground, in inches, can be represented by the trigonometric function f(t) = −13cos(0.8πt) + 13, where t represents the time (in seconds) since the nail first became caught in the tire. Determine the period of f(t). Interpret what the period represents in this context. On the grid below, graph at least one cycle of f(t) that includes the y-intercept of the function.

Does the height of the nail ever reach 30 inches above the ground? Justify your answer.

170 A scatterplot showing the weight, w, in grams, of each crystal after growing t hours is shown below.

The relationship between weight, w, and time, t, is best modeled by1) w = 4t + 52) w = (1.4) t + 23) w = 5(2.1) t

4) w = 8(.75) t

171 Sarah is fighting a sinus infection. Her doctor prescribed a nasal spray and an antibiotic to fight the infection. The active ingredients, in milligrams, remaining in the bloodstream from the nasal spray, n(t), and the antibiotic, a(t), are modeled in the functions below, where t is the time in hours since the medications were taken.

n(t) = t + 1t + 5 + 18

t2 + 8t + 15

a(t) = 9t + 3

Determine which drug is made with a greater initial amount of active ingredient. Justify your answer. Sarah's doctor told her to take both drugs at the same time. Determine algebraically the number of hours after taking the medications when both medications will have the same amount of active ingredient remaining in her bloodstream.


32

172 The solution of 87e 0.3x = 5918, to the nearest thousandth, is1) 0.5832) 1.9453) 4.2204) 14.066

173 Which value, to the nearest tenth, is the smallest

solution of f(x) = g(x) if f(x) = 3sin 12 x

− 1 and

g(x) = x3 − 2x + 1?1) −3.62) −2.13) −1.84) 1.4

174 Graph f(x) = log2(x + 6) on the set of axes below.

175 Suppose events A and B are independent and P(A and B) is 0.2. Which statement could be true?1) P(A) = 0.4, P(B) = 0.3, P(A or B) = 0.52) P(A) = 0.8, P(B) = 0.253) P(A| B) = 0.2, P(B) = 0.24) P(A) = 0.15, P(B) = 0.05

176 A manufacturing plant produces two different-sized containers of peanuts. One container weighs x ounces and the other weighs y pounds. If a gift set can hold one of each size container, which expression represents the number of gift sets needed to hold 124 ounces?

1) 12416x + y

2)x + 16y

124

3) 124x + 16y

4)16x + y

124

177 a) Algebraically determine the roots, in simplest a + bi form, to the equation below.

x 2 − 2x + 7 = 4x − 10b) Consider the system of equations below.

y = x2 − 2x + 7y = 4x − 10

The graph of this system confirms the solution from part a is imaginary. Explain why.

178 Expressed in simplest a + bi form, (7 − 3i) + (x − 2i)2 − (4i + 2x2 ) is1) (3 − x2) − (4x + 7)i2) (3 + 3x2 ) − (4x + 7)i3) (3 − x2) − 7i4) (3 + 3x2 ) − 7i


33

179 Write an equation for a sine function with an

amplitude of 2 and a period of π2 . On the grid

below, sketch the graph of the equation in the interval 0 to 2π .

180 Chuck's Trucking Company has decided to initiate an Employee of the Month program. To determine the recipient, they put the following sign on the back of each truck.

The driver who receives the highest number of positive comments will win the recognition. Explain one statistical bias in this data collection method.

181 Solve the given equation algebraically for all values of x. 3 x − 2x = −5

182 Which table best represents an exponential relationship?

1)

2)

3)

4)


34

183 After Roger’s surgery, his doctor administered pain medication in the following amounts in milligrams over four days.

Day (n) 1 2 3 4Dosage (m) 2000 1680 1411.2 1185.4

How can this sequence best be modeled recursively?1) m1 = 2000

mn = mn − 1 − 320

3) m1 = 2000

mn = (0.84)mn − 1

2) mn = 2000(0.84)n − 1 4) mn = 2000(0.84)n + 1

184 The zeros of a quartic polynomial function are 2, −2, 4, and −4. Use the zeros to construct a possible sketch of the function, on the set of axes below.

185 The average monthly temperature of a city can be modeled by a cosine graph. Melissa has been living in Phoenix, Arizona, where the average annual temperature is 75°F. She would like to move, and live in a location where the average annual temperature is 62°F. When examining the graphs of the average monthly temperatures for various locations, Melissa should focus on the1) amplitude2) horizontal shift3) period4) midline

186 For a given time, x, in seconds, an electric current, y, can be represented by y = 2.5 1 − 2.7−.10x

.

Which equation is not equivalent?1) y = 2.5− 2.5 2.7−.10x

2) y = 2.5− 2.5 2.72

−.05x

3) y = 2.5− 2.5 12.7.10x

4) y = 2.5− 2.5 2.7−2

2.7.05x

187 What is the solution when the equation wx 2 +w = 0 is solved for x, where w is a positive integer?1) −12) 03) 64) ±i

188 For which values of x, rounded to the nearest hundredth, will x2 − 9|

||| − 3 = log3x?

1) 2.29 and 3.632) 2.37 and 3.543) 2.84 and 3.174) 2.92 and 3.06


35

189 Juan and Filipe practice at the driving range before playing golf. The number of wins and corresponding practice times for each player are shown in the table below.

Juan Wins Felipe WinsShort Practice Time 8 10Long Practice Time 15 12

Given that the practice time was long, determine the exact probability that Filipe wins the next match. Determine whether or not the two events “Filipe wins” and “long practice time” are independent. Justify your answer.

190 Graph t(x) = 3sin(2x) + 2 over the domain [0,2π] on the set of axes below.

191 The weights of bags of Graseck's Chocolate Candies are normally distributed with a mean of 4.3 ounces and a standard deviation of 0.05 ounces. What is the probability that a bag of these chocolate candies weighs less than 4.27 ounces?1) 0.22572) 0.27433) 0.72574) 0.7757

192 In a random sample of 250 men in the United States, age 21 or older, 139 are married. The graph below simulated samples of 250 men, 200 times, assuming that 139 of the men are married.

a) Based on the simulation, create an interval in which the middle 95% of the number of married men may fall. Round your answer to the nearest integer. b) A study claims "50 percent of men 21 and older in the United States are married." Do your results from part a contradict this claim? Explain.


36

193 Which graph represents a polynomial function that contains x2 + 2x + 1 as a factor?

1)

2)

3)

4)

194 Susan won $2,000 and invested it into an account with an annual interest rate of 3.2%. If her investment were compounded monthly, which expression best represents the value of her investment after t years?1) 2000(1.003)12t

2) 2000(1.032)t

12

3) 2064t

12

4)2000(1.032) t

12

195 The expression 9x2 − 23x + 1 is equivalent to

1) 3x − 1 − 13x + 1

2) 3x − 1 + 13x + 1

3) 3x + 1 − 13x + 1

4) 3x + 1 + 13x + 1

196 An estimate of the number of milligrams of a medication in the bloodstream t hours after 400 mg has been taken can be modeled by the function below.

I(t) = 0.5t4 + 3.45t3 − 96.65t2 + 347.7t ,where 0 ≤ t ≤ 6

Over what time interval does the amount of medication in the bloodstream strictly increase?1) 0 to 2 hours2) 0 to 3 hours3) 2 to 6 hours4) 3 to 6 hours


37

197 A 4th degree polynomial has zeros −5, 3, i, and −i. Which graph could represent the function defined by this polynomial?

1)

2)

3)

4)

198 The half-life of iodine-131 is 8 days. The percent of the isotope left in the body d days after being

introduced is I = 100 12

d8

. When this equation is

written in terms of the number e, the base of the natural logarithm, it is equivalent to I = 100ekd . What is the approximate value of the constant, k?1) −0.0872) 0.0873) −11.5424) 11.542

199 Write a recursive formula, a n , to describe the sequence graphed below.

200 The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed. Given this information, the approximate percentage of the population with an IQ greater than 130 is closest to1) 2%2) 31%3) 48%4) 95%


38

201 The Beaufort Wind Scale was devised by British Rear Admiral Sir Francis Beaufort, in 1805 based upon observations of the effects of the wind. Beaufort numbers, B, are determined by the equation B = 1.69 s + 4.45 − 3.49, where s is the speed of the wind in mph, and B is rounded to the nearest integer from 0 to 12.

Beaufort Wind ScaleBeaufort Number Force of Wind

0 Calm1 Light air2 Light breeze3 Gentle breeze4 Moderate breeze5 Fresh breeze6 Steady breeze7 Moderate gale8 Fresh gale9 Strong gale10 Whole gale11 Storm12 Hurricane

Using the table above, classify the force of wind at a speed of 30 mph. Justify your answer. In 1946, the scale was extended to accommodate strong hurricanes. A strong hurricane received a B value of exactly 15. Algebraically determine the value of s, to the nearest mph. Any B values that round to 10 receive a Beaufort number of 10. Using technology, find an approximate range of wind speeds, to the nearest mph, associated with a Beaufort number of 10.

202 Judith puts $5000 into an investment account with interest compounded continuously. Which approximate annual rate is needed for the account to grow to $9110 after 30 years?1) 2%2) 2.2%3) 0.02%4) 0.022%

203 A 7-year lease for office space states that the annual rent is $85,000 for the first year and will increase by 6% each additional year of the lease. What will the total rent expense be for the entire 7-year lease?1) $42,809.632) $90,425.533) $595,000.004) $713,476.20


39

204 Consider the function p(x) = 3x3 + x2 − 5x and the graph of y = m(x) below.

Which statement is true?1) p(x) has three real roots and m(x) has two real

roots.2) p(x) has one real root and m(x) has two real

roots.3) p(x) has two real roots and m(x) has three real

roots.4) p(x) has three real roots and m(x) has four real

roots.

205 A recursive formula for the sequence 40,30,22.5,. . . is

1) gn = 40 34

n

2) g 1 = 40

gn = gn − 1 − 10

3) gn = 40 34

n − 1

4) g 1 = 40

gn =34 gn − 1

206 The half-life of a radioactive substance is 15 years. Write an equation that can be used to determine the amount, s(t), of 200 grams of this substance that remains after t years. Determine algebraically, to

the nearest year, how long it will take for 110 of

this substance to remain.

207 What is the solution set of the following system of equations? y = 3x + 6

y = (x + 4)2 − 101) {(−5,−9)}2) {(5,21)}3) {(0,6),(−5,−9)}4) {(0,6),(5,21)}

208 Sketch the graphs of r(x) = 1x and a(x) = x| | − 3 on

the set of axes below. Determine, to the nearest tenth, the positive solution of r(x) = a(x).


40

209 Which sketch best represents the graph of x = 3 y ?

1)

2)

3)

4)

210 Solve the following system of equations algebraically for all values of x, y, and z:

2x + 3y − 4z = −1

x − 2y + 5z = 3

−4x + y + z = 16

211 If a solution of 2(2x − 1) = 5x2 is expressed in simplest a + bi form, the value of b is

1)6

5 i

2)6

5

3) 15 i

4) 15

212 The function N(x) = 90(0.86)x + 69 can be used to predict the temperature of a cup of hot chocolate in degrees Fahrenheit after x minutes. What is the approximate average rate of change of the temperature of the hot chocolate, in degrees per minute, over the interval [0,6]?1) −8.932) −0.113) 0.114) 8.93

213 Consider the system of equations below:

x + y − z = 6

2x − 3y + 2z = −19

−x + 4y − z = 17

Which number is not the value of any variable in the solution of the system?1) −12) 23) 34) −4


41

214 On July 21, 2016, the water level in Puget Sound, WA reached a high of 10.1 ft at 6 a.m. and a low of −2 ft at 12:30 p.m. Across the country in Long Island, NY, Shinnecock Bay’s water level reached a high of 2.5 ft at 10:42 p.m. and a low of −0.1 ft at 5:31 a.m. The water levels of both locations are affected by the tides and can be modeled by sinusoidal functions. Determine the difference in amplitudes, in feet, for these two locations.

215 Erin and Christa were working on cubing binomials for math homework. Erin believed they could save time with a shortcut. She wrote down the rule below for Christa to follow.

(a + b)3 = a 3 + b 3

Does Erin's shortcut always work? Justify your result algebraically.

216 Which expression is equivalent to x6 y4(x4 − 16) − 9(x4 − 16)?1) x10 y 4 − 16x6 y 4 − 9x4 − 1442) (x6 y4 − 9)(x + 2)3(x − 2)3) (x 3 y2 + 3)(x3 y 2 − 3)(x + 2)2 (x − 2)2

4) (x 3 y2 + 3)(x3 y 2 − 3)(x2 + 4)(x2 − 4)

217 What is the solution set of the equation 10

x2 − 2x+ 4

x = 5x − 2 ?

1) 0,2 2) 0 3) 2 4) { }

218 The probability that a resident of a housing community opposes spending money for community improvement on plumbing issues is 0.8. The probability that a resident favors spending money on improving walkways given that the resident opposes spending money on plumbing issues is 0.85. Determine the probability that a randomly selected resident opposes spending money on plumbing issues and favors spending money on walkways.

219 After examining the functions f(x) = ln(x + 2) and g(x) = ex − 1 over the interval (−2,3], Lexi determined that the correct number of solutions to the equation f(x) = g(x) is1) 12) 23) 34) 0

220 What is the equation of the directrix for the parabola −8(y − 3) = (x + 4)2?1) y = 52) y = 13) y = −24) y = −6

221 Perry invested in property that cost him $1500. Five years later it was worth $3000, and 10 years from his original purchase, it was worth $6000. Assuming the growth rate remains the same, which type of function could he create to find the value of his investment 30 years from his original purchase?1) exponential function2) linear function3) quadratic function4) trigonometric function


42

222 The temperature, in degrees Fahrenheit, in Times Square during a day in August can be predicted by the function T(x) = 8sin(0.3x − 3) + 74, where x is the number of hours after midnight. According to this model, the predicted temperature, to the nearest degree Fahrenheit, at 7 P.M. is1) 682) 743) 774) 81

223 The completely factored form of n 4 − 9n 2 + 4n 3 − 36n − 12n 2 + 108 is1) (n 2 − 9)(n + 6)(n − 2)2) (n + 3)(n − 3)(n + 6)(n − 2)3) (n − 3)(n − 3)(n + 6)(n − 2)4) (n + 3)(n − 3)(n − 6)(n + 2)

224 Robin flips a coin 100 times. It lands heads up 43 times, and she wonders if the coin is unfair. She runs a computer simulation of 750 samples of 100 fair coin flips. The output of the proportion of heads is shown below.

Do the results of the simulation provide strong evidence that Robin’s coin is unfair? Explain your answer.

225 The depth of the water at a marker 20 feet from the shore in a bay is depicted in the graph below.

If the depth, d, is measured in feet and time, t, is measured in hours since midnight, what is an equation for the depth of the water at the marker?

1) d = 5cos π6 t

+ 9

2) d = 9cos π6 t

+ 5

3) d = 9sin π6 t

+ 5

4) d = 5sin π6 t

+ 9

226 For x ≥ 0, which equation is false?

1) (x32 )2 = x34

2) (x3 )14 = x34

3) (x32 )

12 = x 34

4) (x23 )2 = x43


43

227 Consider the function h(x) = 2sin(3x) + 1 and the function q represented in the table below.

x q(x)−2 −8−1 00 01 −22 0

Determine which function has the smaller minimum value for the domain [−2,2]. Justify your answer.

228 A population of 950 bacteria grows continuously at a rate of 4.75% per day. Write an exponential function, N(t), that represents the bacterial population after t days and explain the reason for your choice of base. Determine the bacterial population after 36 hours, to the nearest bacterium.

229 The operator of the local mall wants to find out how many of the mall's employees make purchases in the food court when they are working. She hopes to use these data to increase the rent and attract new food vendors. In total, there are 1023 employees who work at the mall. The best method to obtain a random sample of the employees would be to survey1) all 170 employees at each of the larger stores2) 50% of the 90 employees of the food court3) every employee4) every 30th employee entering each mall

entrance for one week

230 Over the set of integers, factor the expression x4 − 4x2 − 12.

231 On a given school day, the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps and has a pop quiz on the same day?1) 73%2) 36%3) 23%4) 12%

232 Kelly-Ann has $20,000 to invest. She puts half of the money into an account that grows at an annual rate of 0.9% compounded monthly. At the same time, she puts the other half of the money into an account that grows continuously at an annual rate of 0.8%. Which function represents the value of Kelly-Ann's investments after t years?1) f(t) = 10,000(1.9) t + 10,000e0.8t

2) f(t) = 10,000(1.009) t + 10,000e0.008t

3) f(t) = 10,000(1.075)12t + 10,000e 0.8t

4) f(t) = 10,000(1.00075)12t + 10,000e 0.008t


44

233 Tony is evaluating his retirement savings. He currently has $318,000 in his account, which earns an interest rate of 7% compounded annually. He wants to determine how much he will have in the account in the future, even if he makes no additional contributions to the account. Write a function, A(t), to represent the amount of money that will be in his account in t years. Graph A(t) where 0 ≤ t ≤ 20 on the set of axes below.

Tony's goal is to save $1,000,000. Determine algebraically, to the nearest year, how many years it will take for him to achieve his goal. Explain how your graph of A(t) confirms your answer.

234 Which equation represents the equation of the parabola with focus (−3,3) and directrix y = 7?

1) y = 18 (x + 3)2 − 5

2) y = 18 (x − 3)2 + 5

3) y = −18 (x + 3)2 + 5

4) y = −18 (x − 3)2 + 5

235 At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the nth term of this sequence is an = 25,000 + (n − 1)1000. Which rule best represents the equivalent recursive formula?1) an = 24,000+ 1000n2) an = 25,000+ 1000n3) a 1 = 25,000, an = an − 1 + 10004) a 1 = 25,000, an = an + 1 + 1000

236 When the expression (x + 2)2 + 4(x + 2) + 3 is rewritten as the product of two binomials, the result is1) (x + 3)(x + 1)2) (x + 5)(x + 3)3) (x + 2)(x + 2)4) (x + 6)(x + 1)

237 At Andrew Jackson High School, students are only allowed to enroll in AP U.S. History if they have already taken AP World History or AP European History. Out of 825 incoming seniors, 165 took AP World History, 66 took AP European History, and 33 took both. Given this information, determine the probability a randomly selected incoming senior is allowed to enroll in AP U.S. History.

238 When factoring to reveal the roots of the equation x 3 + 2x 2 − 9x − 18 = 0, which equations can be used? I. x2 (x + 2) − 9(x + 2) = 0 II. x(x2 − 9) + 2(x 2 − 9) = 0 III. (x − 2)(x2 − 9) = 01) I and II, only2) I and III, only3) II and III, only4) I, II, and III


45

Algebra II Regents at Random

239 The loudness of sound is measured in units called decibels (dB). These units are measured by first assigning an intensity I0 to a very soft sound that is called the threshold sound. The sound to be measured is assigned an

intensity, I, and the decibel rating, d, of this sound is found using d = 10log II0

. The threshold sound audible to

the average person is 1.0× 10−12 W/m2 (watts per square meter). Consider the following sound level classifications:

Moderate 45-69 dBLoud 70-89 dBVery loud 90-109 dBDeafening >110 dB

How would a sound with intensity 6.3× 10−3 W/m2 be classified?1) moderate 3) very loud2) loud 4) deafening

240 Find algebraically the zeros for p(x) = x3 + x 2 − 4x − 4. On the set of axes below, graph y = p(x).

241 The solution set for the equation 56− x = x is1) {−8,7}2) {−7,8}3) {7}4) { }

242 The function p(t) = 110e0.03922t models the population of a city, in millions, t years after 2010. As of today, consider the following two statements: I. The current population is 110 million. II. The population increases continuously by approximately 3.9% per year.This model supports1) I, only2) II, only3) both I and II4) neither I nor II


46

243 An orange-juice processing plant receives a truckload of oranges. The quality control team randomly chooses three pails of oranges, each containing 50 oranges, from the truckload. Identify the sample and the population in the given scenario. State one conclusion that the quality control team could make about the population if 5% of the sample was found to be unsatisfactory.

244 If g(c) = 1 − c 2 and m(c) = c + 1, then which statement is not true?1) g(c) ⋅m(c) = 1+ c − c2 − c3

2) g(c) +m(c) = 2+ c − c 2

3) m(c) − g(c) = c + c2

4)m(c)g(c) = −1

1 − c

245 Which equation is represented by the graph shown below?

1) y = 12 cos 2x

2) y = cos x

3) y = 12 cos x

4) y = 2cos 12 x

246 Which equation represents an odd function?1) y = sinx2) y = cos x3) y = (x + 1)3

4) y = e5x

247 Given the geometric series 300+ 360 + 432+ 518.4 +. . . , write a geometric series formula, S n, for the sum of the first n terms. Use the formula to find the sum of the first 10 terms, to the nearest tenth.

248 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year. Write a geometric series formula, S n , for Alexa's total earnings over n years. Use this formula to find Alexa's total earnings for her first 15 years of teaching, to the nearest cent.

249 What is the solution, if any, of the equation 2

x + 3 − 34 − x = 2x − 2

x2 − x − 12?

1) −12) −53) all real numbers4) no real solution

250 The heights of women in the United States are normally distributed with a mean of 64 inches and a standard deviation of 2.75 inches. The percent of women whose heights are between 64 and 69.5 inches, to the nearest whole percent, is1) 62) 483) 684) 95


47

251 Given f(9) = −2, which function can be used to generate the sequence −8,−7.25,−6.5,−5.75,. . .?1) f(n) = −8 + 0.75n2) f(n) = −8 − 0.75(n − 1)3) f(n) = −8.75+ 0.75n4) f(n) = −0.75 + 8(n − 1)

252 For n and p > 0, is the expression

p 2n12

8

p 5 n 4 equivalent to p 18 n 6 p ?

Justify your answer.

253 Using the formula below, determine the monthly payment on a 5-year car loan with a monthly percentage rate of 0.625% for a car with an original cost of $21,000 and a $1000 down payment, to the nearest cent.

Pn = PMT1 − (1+ i)−n

i

Pn = present amount borrowedn = number of monthly pay periods

PMT = monthly paymenti = interest rate per month

The affordable monthly payment is $300 for the same time period. Determine an appropriate down payment, to the nearest dollar.

254 Use an appropriate procedure to show that x − 4 is a factor of the function f(x) = 2x 3 − 5x 2 − 11x − 4. Explain your answer.

255 Drugs break down in the human body at different rates and therefore must be prescribed by doctors carefully to prevent complications, such as overdosing. The breakdown of a drug is represented by the function N(t) = N0 (e)−rt , where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligrams of a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug with a decay rate of 0.231. Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given to each patient. Graph each function on the set of axes below.

To the nearest hour, t, when does the amount of the given drug remaining in patient B begin to exceed the amount of the given drug remaining in patient A? The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient A will have to wait to take another 800 milligram dose of the drug.


48

256 The distance needed to stop a car after applying the brakes varies directly with the square of the car’s speed. The table below shows stopping distances for various speeds.

Speed (mph) 10 20 30 40 50 60 70Distance (ft) 6.25 25 56.25 100 156.25 225 306.25

Determine the average rate of change in braking distance, in ft/mph, between one car traveling at 50 mph and one traveling at 70 mph. Explain what this rate of change means as it relates to braking distance.

257 The guidance department has reported that of the senior class, 2.3% are members of key club, K, 8.6% are enrolled in AP Physics, P, and 1.9% are in both. Determine the probability of P given K, to the nearest tenth of a percent. The principal would like a basic interpretation of these results. Write a statement relating your calculated probabilities to student enrollment in the given situation.

258 One of the medical uses of Iodine–131 (I–131), a radioactive isotope of iodine, is to enhance x-ray images. The half-life of I–131 is approximately 8.02 days. A patient is injected with 20 milligrams of I–131. Determine, to the nearest day, the amount of time needed before the amount of I–131 in the patient’s body is approximately 7 milligrams.

259 A radioactive substance has a mass of 140 g at 3 p.m. and 100 g at 8 p.m. Write an equation in the

form A = A012

th

that models this situation,

where h is the constant representing the number of hours in the half-life, A0 is the initial mass, and A is the mass t hours after 3 p.m. Using this equation, solve for h, to the nearest ten thousandth. Determine when the mass of the radioactive substance will be 40 g. Round your answer to the nearest tenth of an hour.

260 Given i is the imaginary unit, (2 − yi)2 in simplest form is1) y2 − 4yi + 42) −y2 − 4yi + 43) −y2 + 44) y2 + 4

261 Which function represents exponential decay?1) y = 20.3t

2) y = 1.23t

3) y = 12

−t

4) y = 5−t

262 Cheap and Fast gas station is conducting a consumer satisfaction survey. Which method of collecting data would most likely lead to a biased sample?1) interviewing every 5th customer to come into

the station2) interviewing customers chosen at random by a

computer at the checkout3) interviewing customers who call an 800

number posted on the customers' receipts4) interviewing every customer who comes into

the station on a day of the week chosen at random out of a hat


49

263 Jim is looking to buy a vacation home for $172,600 near his favorite southern beach. The formula to compute a mortgage payment, M, is

M = P •r(1 + r) N

(1+ r) N − 1 where P is the principal

amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Jim's bank offers a monthly interest rate of 0.305% for a 15-year mortgage. With no down payment, determine Jim's mortgage payment, rounded to the nearest dollar. Algebraically determine and state the down payment, rounded to the nearest dollar, that Jim needs to make in order for his mortgage payment to be $1100.

264 The directrix of the parabola 12(y + 3) = (x − 4)2 has the equation y = −6. Find the coordinates of the focus of the parabola.

265 The expression 4x 3 + 5x + 102x + 3 is equivalent to

1) 2x2 + 3x − 7+ 312x + 3

2) 2x2 − 3x + 7− 112x + 3

3) 2x 2 + 2.5x + 5+ 152x + 3

4) 2x 2 − 2.5x − 5− 202x + 3

266 Describe how a controlled experiment can be created to examine the effect of ingredient X in a toothpaste.

267 The parabola y = − 120 (x − 3)2 + 6 has its focus at

(3,1). Determine and state the equation of the directrix. (The use of the grid below is optional.)

268 A polynomial equation of degree three, p(x), is used to model the volume of a rectangular box. The graph of p(x) has x intercepts at −2, 10, and 14. Which statements regarding p(x) could be true?A. The equation of p(x) = (x − 2)(x + 10)(x + 14).B. The equation of p(x) = −(x + 2)(x − 10)(x − 14).C. The maximum volume occurs when x = 10.D. The maximum volume of the box is approximately 56.1) A and C2) A and D3) B and C4) B and D


50

269 If a, b, and c are all positive real numbers, which graph could represent the sketch of the graph of p(x) = −a(x + b) x 2 − 2cx + c2

?

1)

2)

3)

4)

270 The expression x 3 + 2x2 + x + 6x + 2 is equivalent to

1) x2 + 3

2) x2 + 1 + 4x + 2

3) 2x2 + x + 6

4) 2x 2 + 1+ 4x + 2

271 There was a study done on oxygen consumption of snails as a function of pH, and the result was a degree 4 polynomial function whose graph is shown below.

Which statement about this function is incorrect?1) The degree of the polynomial is even.2) There is a positive leading coefficient.3) At two pH values, there is a relative maximum

value.4) There are two intervals where the function is

decreasing.


51

272 Functions f, g, and h are given below.

f(x) = sin(2x)

g(x) = f(x) + 1

Which statement is true about functions f, g, and h?1) f(x) and g(x) are odd, h(x) is even.2) f(x) and g(x) are even, h(x) is odd.3) f(x) is odd, g(x) is neither, h(x) is even.4) f(x) is even, g(x) is neither, h(x) is odd.

273 The inverse of the function f(x) = x + 1x − 2 is

1) f − 1 (x) = x + 1x + 2

2) f − 1 (x) = 2x + 1x − 1

3) f − 1 (x) = x + 1x − 2

4) f − 1 (x) = x − 1x + 1

274 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band. Members of the prom committee thought that the vote would have 50% for the DJ and 50% for the band. A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.

Using the results of the simulation, determine a plausible interval containing the middle 95% of the data. Round all values to the nearest hundredth. Members of the prom committee are concerned that a vote of all students attending the prom may produce a 50% − 50% split. Explain what statistical evidence supports this concern.

275 Using the identity sin2θ + cos2θ = 1, find the value of tanθ , to the nearest hundredth, if cosθ is –0.7 and θ is in Quadrant II.

276 Solve algebraically for all values of x: x − 5 + x = 7


52

277 Seventy-two students are randomly divided into two equally-sized study groups. Each member of the first group (group 1) is to meet with a tutor after school twice each week for one hour. The second group (group 2), is given an online subscription to a tutorial account that they can access for a maximum of two hours each week. Students in both groups are given the same tests during the year. A summary of the two groups’ final grades is shown below:

Group 1 Group 2x 80.16 83.8S x 6.9 5.2

Calculate the mean difference in the final grades (group 1 – group 2) and explain its meaning in the context of the problem. A simulation was conducted in which the students’ final grades were rerandomized 500 times. The results are shown below.

Use the simulation to determine if there is a significant difference in the final grades. Explain your answer.

278 The voltage used by most households can be modeled by a sine function. The maximum voltage is 120 volts, and there are 60 cycles every second. Which equation best represents the value of the voltage as it flows through the electric wires, where t is time in seconds?1) V = 120sin(t)2) V = 120sin(60t)3) V = 120sin(60πt)4) V = 120sin(120πt)

279 Last year, the total revenue for Home Style, a national restaurant chain, increased 5.25% over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let m represent months.]1) (1.0525)m

2) (1.0525)12m

3) (1.00427)m

4) (1.00427)m12


53

280 In 2010, the population of New York State was approximately 19,378,000 with an annual growth rate of 1.5%. Assuming the growth rate is maintained for a large number of years, which equation can be used to predict the population of New York State t years after 2010?1) Pt = 19,378,000(1.5) t

2) P0 = 19,378,000

Pt = 19,378,000+ 1.015Pt − 1

3) Pt = 19,378,000(1.015) t − 1

4) P0 = 19,378,000

Pt = 1.015Pt − 1

281 Which sinusoid has the greatest amplitude?

1)2) y = 3sin(θ − 3) + 5

3)4) y = −5sin(θ − 1) − 3

282 Given r(x) = x3 − 4x2 + 4x − 6, find the value of r(2). What does your answer tell you about x − 2 as a factor of r(x)? Explain.

283 The equation 4x2 − 24x + 4y 2 + 72y = 76 is equivalent to1) 4(x − 3)2 + 4(y + 9)2 = 762) 4(x − 3)2 + 4(y + 9)2 = 1213) 4(x − 3)2 + 4(y + 9)2 = 1664) 4(x − 3)2 + 4(y + 9)2 = 436

284 The function f(x) = x − 3x2 + 2x − 8

is undefined when

x equals1) 2 or − 42) 4 or − 23) 3, only4) 2, only

285 What does −54x9

y4

23

equal?

1)9ix6 43

y y23

2)9ix6 43

y 2 y 23

3)9x 6 43

y y3

4)9x 6 43

y 2 y 23

286 `Solve the system of equations shown below algebraically.

(x − 3)2 + (y + 2)2 = 16

2x + 2y = 10


54

287 Charlie's Automotive Dealership is considering implementing a new check-in procedure for customers who are bringing their vehicles for routine maintenance. The dealership will launch the procedure if 50% or more of the customers give the new procedure a favorable rating when compared to the current procedure. The dealership devises a simulation based on the minimal requirement that 50% of the customers prefer the new procedure. Each dot on the graph below represents the proportion of the customers who preferred the new check-in procedure, each of sample size 40, simulated 100 times.

Assume the set of data is approximately normal and the dealership wants to be 95% confident of its results. Determine an interval containing the plausible sample values for which the dealership will launch the new procedure. Round your answer to the nearest hundredth. Forty customers are selected randomly to undergo the new check-in procedure and the proportion of customers who prefer the new procedure is 32.5%. The dealership decides not to implement the new check-in procedure based on the results of the study. Use statistical evidence to explain this decision.

288 The focal length, F, of a camera’s lens is related to the distance of the object from the lens, J, and the distance to the image area in the camera, W, by the formula below.

1J + 1

W = 1F

When this equation is solved for J in terms of F and W, J equals1) F −W

2) FWF −W

3) FWW− F

4) 1F − 1

W

289 Elizabeth waited for 6 minutes at the drive thru at her favorite fast-food restaurant the last time she visited. She was upset about having to wait that long and notified the manager. The manager assured her that her experience was very unusual and that it would not happen again. A study of customers commissioned by this restaurant found an approximately normal distribution of results. The mean wait time was 226 seconds and the standard deviation was 38 seconds. Given these data, and using a 95% level of confidence, was Elizabeth’s wait time unusual? Justify your answer.


55

290 Monthly mortgage payments can be found using the formula below:

M =

P r12

1 + r12

n

1+ r12

n

− 1

M = monthly paymentP = amount borrowedr = annual interest rate

n = number of monthly payments

The Banks family would like to borrow $120,000 to purchase a home. They qualified for an annual interest rate of 4.8%. Algebraically determine the fewest number of whole years the Banks family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720.

291 If the terminal side of angle , in standard position, passes through point (−4,3), what is the numerical value of sinθ ?

1) 35

2) 45

3) −35

4) −45

292 Given: h(x) = 29 x3 + 8

9 x2 − 1613 x + 2

k(x) = − 0.7x| | + 5State the solutions to the equation h(x) = k(x), rounded to the nearest hundredth.

293 Rewrite the expression

4x2 + 5x

2− 5 4x2 + 5x

− 6 as a product of four

linear factors.

294 A solution of the equation 2x 2 + 3x + 2 = 0 is

1) −34 + 1

4 i 7

2) −34 + 1

4 i

3) −34 + 1

4 7

4) 12

295 Given the parent function p(x) = cos x, which phrase best describes the transformation used to obtain the graph of g(x) = cos(x + a) − b , if a and b are positive constants?1) right a units, up b units2) right a units, down b units3) left a units, up b units4) left a units, down b units

296 When b > 0 and d is a positive integer, the

expression (3b)2d is equivalent to

1) 1

3bd

2

2) 3b

d

3) 1

3bd

4) 3bd

2


56

297 When g(x) = 2x + 2 and h(x) = log(x + 1) + 3 are

graphed on the same set of axes, which coordinates best approximate their point of intersection?1) (−0.9,1.8)2) (−0.9,1.9)3) (1.4,3.3)4) (1.4,3.4)

298 Pedro and Bobby each own an ant farm. Pedro starts with 100 ants and says his farm is growing exponentially at a rate of 15% per month. Bobby starts with 350 ants and says his farm is steadily decreasing by 5 ants per month. Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants?1) 72) 83) 134) 36

299 A recursive formula for the sequence 18,9,4.5,. . . is1) g 1 = 18

gn =12 gn − 1

2) gn = 18 12

n − 1

3) g 1 = 18

gn = 2gn − 1

4) gn = 18 2 n − 1

300 Solve for x: 1x − 1

3 = − 13x

301 Which equation represents the set of points equidistant from line and point R shown on the graph below?

1) y = −18 (x + 2)2 + 1

2) y = −18 (x + 2)2 − 1

3) y = −18 (x − 2)2 + 1

4) y = −18 (x − 2)2 − 1

302 What is the inverse of the function y = log3x?1) y = x3

2) y = logx 33) y = 3x

4) x = 3 y

303 Which statement about the graph of c(x) = log6x is false?1) The asymptote has equation y = 0.2) The graph has no y-intercept.3) The domain is the set of positive reals.4) The range is the set of all real numbers.


57

304 The solutions to the equation −12 x 2 = −6x + 20 are

1) −6 ± 2i2) −6 ± 2 193) 6 ± 2i4) 6 ± 2 19


x + y + z = 1

2x + 4y + 6z = 2

−x + 3y − 5z = 11

306 Which statement(s) about statistical studies is true?I. A survey of all English classes in a high

school would be a good sample to determine the number of hours students throughout the school spend studying.

II. A survey of all ninth graders in a high school would be a good sample to determine the number of student parking spaces needed at that high school.

III. A survey of all students in one lunch period in a high school would be a good sample to determine the number of hours adults spend on social media websites.

IV. A survey of all Calculus students in a high school would be a good sample to determine the number of students throughout the school who don’t like math.

1) I, only2) II, only3) I and III4) III and IV

307 To solve 2xx − 2 − 11

x = 8x 2 − 2x

, Ren multiplied

both sides by the least common denominator. Which statement is true?1) 2 is an extraneous solution.

2) 72 is an extraneous so1ution.

3) 0 and 2 are extraneous solutions.4) This equation does not contain any extraneous

solutions.

308 On the axes below, graph one cycle of a cosine

function with amplitude 3, period π2 , midline

y = −1, and passing through the point (0,2).

309 Write an explicit formula for a n , the nth term of the recursively defined sequence below.

a 1 = x + 1

an = x(an − 1 )For what values of x would an = 0 when n > 1?


58


x + 3y + 5z = 45

6x − 3y + 2z = −10

−2x + 3y + 8z = 72

311 A candidate for political office commissioned a poll. His staff received responses from 900 likely voters and 55% of them said they would vote for the candidate. The staff then conducted a simulation of 1000 more polls of 900 voters, assuming that 55% of voters would vote for their candidate. The output of the simulation is shown in the diagram below.

Given this output, and assuming a 95% confidence level, the margin of error for the poll is closest to1) 0.012) 0.033) 0.064) 0.12

312 Simplify xi(i − 7i)2 , where i is the imaginary unit.

313 Factored completely, m5 +m3 − 6m is equivalent to1) (m+ 3)(m− 2)2) (m2 + 3m)(m2 − 2)3) m(m4 +m2 − 6)4) m(m2 + 3)(m2 − 2)

314 According to a pricing website, Indroid phones lose 58% of their cash value over 1.5 years. Which expression can be used to estimate the value of a $300 Indroid phone in 1.5 years?1) 300e−0.87

2) 300e−0.63

3) 300e−0.58

4) 300e−0.42

315 In contract negotiations between a local government agency and its workers, it is estimated that there is a 50% chance that an agreement will be reached on the salaries of the workers. It is estimated that there is a 70% chance that there will be an agreement on the insurance benefits. There is a 20% chance that no agreement will be reached on either issue. Find the probability that an agreement will be reached on both issues. Based on this answer, determine whether the agreement on salaries and the agreement on insurance are independent events. Justify your answer.

316 The solution to the equation 4x2 + 98 = 0 is1) ±72) ±7i

3) ±7 2

2

4) ±7i 2

2


59

317 A sine function increasing through the origin can be used to model light waves. Violet light has a wavelength of 400 nanometers. Over which interval is the height of the wave decreasing, only?1) (0,200)2) (100,300)3) (200,400)4) (300,400)

318 To the nearest tenth, the value of x that satisfies 2x = −2x + 11 is1) 2.52) 2.63) 5.84) 5.9

319 Mallory wants to buy a new window air conditioning unit. The cost for the unit is $329.99. If she plans to run the unit three months out of the year for an annual operating cost of $108.78, which function models the cost per year over the lifetime of the unit, C(n), in terms of the number of years, n, that she owns the air conditioner.1) C(n) = 329.99 + 108.78n2) C(n) = 329.99 + 326.34n

3) C(n) = 329.99+ 108.78nn

4) C(n) = 329.99+ 326.34nn

320 Biologists are studying a new bacterium. They create a culture with 100 of the bacteria and anticipate that the number of bacteria will double every 30 hours. Write an equation for the number of bacteria, B, in terms of the number of hours, t, since the experiment began.

321 Which diagram represents an angle, α , measuring 13π20 radians drawn in standard position, and its

reference angle, θ ?

1)

2)

3)

4)

322 What are the zeros of P(m) = (m2 − 4)(m2 + 1)?1) 2 and − 2, only2) 2, − 2, and − 43) −4, i, and − i4) 2, − 2, i, and − i


60

323 Ayva designed an experiment to determine the effect of a new energy drink on a group of 20 volunteer students. Ten students were randomly selected to form group 1 while the remaining 10 made up group 2. Each student in group 1 drank one energy drink, and each student in group 2 drank one cola drink. Ten minutes later, their times were recorded for reading the same paragraph of a novel. The results of the experiment are shown below.

Group 1(seconds)

Group 2(seconds)

17.4 23.318.1 18.818.2 22.119.6 12.718.6 16.916.2 24.416.1 21.215.3 21.217.8 16.319.7 14.5

Mean = 17.7 Mean = 19.1

Ayva thinks drinking energy drinks makes students read faster. Using information from the experimental design or the results, explain why Ayva’s hypothesis may be incorrect. Using the given results, Ayva randomly mixes the 20 reading times, splits them into two groups of 10, and simulates the difference of the means 232 times.

Ayva has decided that the difference in mean reading times is not an unusual occurrence. Support her decision using the results of the simulation. Explain your reasoning.


61

324 Which diagram shows an angle rotation of 1 radian on the unit circle?

1)

2)

3)

4)

325 The sequence a 1 = 6, a n = 3an − 1 can also be written as1) an = 6 ⋅ 3n

2) an = 6 ⋅ 3n + 1

3) an = 2 ⋅ 3n

4) an = 2 ⋅ 3n + 1

326 After sitting out of the refrigerator for a while, a turkey at room temperature (68°F) is placed into an oven at 8 a.m., when the oven temperature is 325°F. Newton’s Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven, as given by the formula below:

T = Ta + T0 − Ta

e−kt

Ta = the temperature surrounding the object

T0 = the initial temperature of the object

t = the time in hours

T = the temperature of the object after t hours

k = decay constant

The turkey reaches the temperature of approximately 100° F after 2 hours. Find the value of k, to the nearest thousandth, and write an equation to determine the temperature of the turkey after t hours. Determine the Fahrenheit temperature of the turkey, to the nearest degree, at 3 p.m.

327 Titanium-44 is a radioactive isotope such that every 63 years, its mass decreases by half. For a sample of titanium-44 with an initial mass of 100 grams, write a function that will give the mass of the sample remaining after any amount of time. Define all variables. Scientists sometimes use the average yearly decrease in mass for estimation purposes. Use the average yearly decrease in mass of the sample between year 0 and year 10 to predict the amount of the sample remaining after 40 years. Round your answer to the nearest tenth. Is the actual mass of the sample or the estimated mass greater after 40 years? Justify your answer.


62

328 The price of a postage stamp in the years since the end of World War I is shown in the scatterplot below.

The equation that best models the price, in cents, of a postage stamp based on these data is1) y = 0.59x − 14.822) y = 1.04(1.43)x

3) y = 1.43(1.04)x

4) y = 24sin(14x) + 25

329 Emmeline is working on one side of a polynomial identity proof used to form Pythagorean triples. Her work is shown below:

(5x)2 + (5x2 − 5)2

Step 1: 25x2 + (5x2 − 5)2

Step 2: 25x 2 + 25x2 + 25Step 3: 50x 2 + 25Step 4: 75x2 What statement is true regarding Emmeline's work?1) Emmeline's work is entirely correct.2) There is a mistake in step 2, only.3) There are mistakes in step 2 and step 4.4) There is a mistake in step 4, only.

330 On the axes below, sketch a possible function p(x) = (x − a)(x − b)(x + c), where a, b, and c are positive, a > b, and p(x) has a positive y-intercept of d. Label all intercepts.

331 The graph of the function p(x) is sketched below.

Which equation could represent p(x)?1) p(x) = (x2 − 9)(x − 2)2) p(x) = x3 − 2x2 + 9x + 183) p(x) = (x2 + 9)(x − 2)4) p(x) = x3 + 2x2 − 9x − 18


63

332 A study conducted in 2004 in New York City found that 212 out of 1334 participants had hypertension. Kim ran a simulation of 100 studies based on these data. The output of the simulation is shown in the diagram below.

At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to1) proportion ≈ .16; margin of error ≈ .012) proportion ≈ .16; margin of error ≈ .023) proportion ≈ .01; margin of error ≈ .164) proportion ≈ .02; margin of error ≈ .16

333 An equation to represent the value of a car after t

months of ownership is v = 32,000(0.81)t

12 . Which statement is not correct?1) The car lost approximately 19% of its value

each month.2) The car maintained approximately 98% of its

value each month.3) The value of the car when it was purchased

was $32,000.4) The value of the car 1 year after it was

purchased was $25,920.

334 While experimenting with her calculator, Candy creates the sequence 4, 9, 19, 39, 79, .... Write a recursive formula for Candy's sequence. Determine the eighth term in Candy's sequence.

335 According to a study, 45% of Americans have type O blood. If a random number generator produces three-digit values from 000 to 999, which values would represent those having type O blood?1) between 000 and 045, inclusive2) between 000 and 444, inclusive3) between 000 and 449, inclusive4) between 000 and 450, inclusive

336 The expression 6x3 + 17x2 + 10x + 22x + 3 equals

1) 3x2 + 4x − 1+ 52x + 3

2) 6x2 + 8x − 2+ 52x + 3

3) 6x2 − x + 13− 372x + 3

4) 3x 2 + 13x + 492 + 151

2x + 3

337 Algebraically prove that x 3 + 9x3 + 8

= 1+ 1x 3 + 8

,

where x ≠ −2.

338 What is the solution set of the equation 3x + 25x + 7 − 5 = 3

x ?

1) 32 ,7

2) 72 ,−3

3) −32 ,7

4) −72 ,−3


64

339 Visible light can be represented by sinusoidal waves. Three visible light waves are shown in the graph below. The midline of each wave is labeled .

Based on the graph, which light wave has the longest period? Justify your answer.

340 Data collected about jogging from students with two older siblings are shown in the table below.

Neither SiblingJogs

One SiblingJogs

Both SiblingsJog

Student DoesNot Jog 1168 1823 1380

Student Jogs 188 416 400

Using these data, determine whether a student with two older siblings is more likely to jog if one sibling jogs or if both siblings jog. Justify your answer.

341 Using the unit circle below, explain why csc θ = 1y . 342 A suburban high school has a population of 1376

students. The number of students who participate in sports is 649. The number of students who participate in music is 433. If the probability that a student participates in either sports or music is 9741376, what is the probability that a student

participates in both sports and music?


65

343 Solve the equation 2x − 7 + x = 5 algebraically, and justify the solution set.

344 The graph of p(x) is shown below.

What is the remainder when p(x) is divided by x + 4?1) x − 42) −43) 04) 4

345 Jasmine decides to put $100 in a savings account each month. The account pays 3% annual interest, compounded monthly. How much money, S, will Jasmine have after one year?1) S = 100(1.03)12

2) S =100− 100(1.0025)12

1 − 1.00253) S = 100(1.0025)12

4) S =100 − 100(1.03)12

1− 1.03

346 For the function f x = x − 3 3 + 1, find f −1 x .

347 Which binomial is a factor of x4 − 4x2 − 4x + 8?1) x − 22) x + 23) x − 44) x + 4

348 The population of Jamesburg for the years 2010-2013, respectively, was reported as follows:250,000 250,937 251,878 252,822How can this sequence be recursively modeled?1) j n = 250,000(1.00375)n − 1

2) j n = 250,000+ 937(n − 1)

3) j 1 = 250,000

j n = 1.00375j n − 1

4) j 1 = 250,000

j n = j n − 1 + 937

349 Given f − 1 (x) = −34 x + 2, which equation

represents f(x)?

1) f(x) = 43 x − 8

3

2) f(x) = −43 x + 8

3

3) f(x) = 34 x − 2

4) f(x) = −34 x + 2

350 Given the equal terms x53 and y56 , determine and

state y, in terms of x.


66

351 The results of a survey of the student body at Central High School about television viewing preferences are shown below.

Comedy Series Drama Series Reality Series TotalMales 95 65 70 230Females 80 70 110 260Total 175 135 180 490

Are the events “student is a male” and “student prefers reality series” independent of each other? Justify your answer.

352 Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees F, can be modeled by the equation B(x) = 23.914sin(0.508x − 2.116) + 55.300. The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation P(x) = 20.238sin(0.525x − 2.148) + 86.729. Which statement can not be concluded based on the average monthly temperature models x months after starting data collection?1) The average monthly temperature variation is

more in Bar Harbor than in Phoenix.2) The midline average monthly temperature for

Bar Harbor is lower than the midline temperature for Phoenix.

3) The maximum average monthly temperature for Bar Harbor is 79° F, to the nearest degree.

4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.

353 In New York State, the minimum wage has grown exponentially. In 1966, the minimum wage was $1.25 an hour and in 2015, it was $8.75. Algebraically determine the rate of growth to the nearest percent.

354 The weight of a bag of pears at the local market averages 8 pounds with a standard deviation of 0.5 pound. The weights of all the bags of pears at the market closely follow a normal distribution. Determine what percentage of bags, to the nearest integer, weighed less than 8.25 pounds.

355 A parabola has its focus at (1,2) and its directrix is y = −2. The equation of this parabola could be1) y = 8(x + 1)2

2) y = 18 (x + 1)2

3) y = 8(x − 1)2

4) y = 18 (x − 1)2

356 The function f(x) = 2−0.25x • sin π2 x

represents a

damped sound wave function. What is the average rate of change for this function on the interval [−7,7], to the nearest hundredth?1) −3.662) −0.303) −0.264) 3.36


67

357 Joelle has a credit card that has a 19.2% annual interest rate compounded monthly. She owes a total balance of B dollars after m months. Assuming she makes no payments on her account, the table below illustrates the balance she owes after m months.

m B0 100.0010 1172.0019 1352.0036 1770.8060 2591.9069 2990.0072 3135.8073 3186.00

Over which interval of time is her average rate of change for the balance on her credit card account the greatest?1) month 10 to month 60 3) month 36 to month 722) month 19 to month 69 4) month 60 to month 73

358 If sin2 (32°) + cos2 (M) = 1, then M equals1) 32°2) 58°3) 68°4) 72°

359 Solve for all values of p: 3p

p − 5 − 2p + 3 =

pp + 3

360 Over the set of integers, factor the expression 4x3 − x 2 + 16x − 4 completely.

361 Which factorization is incorrect?1) 4k 2 − 49 = (2k + 7)(2k − 7)2) a 3 − 8b 3 = (a − 2b)(a 2 + 2ab + 4b 2 )3) m3 + 3m2 − 4m+ 12 = (m− 2)2 (m+ 3)4) t3 + 5t2 + 6t + t2 + 5t + 6 = (t + 1)(t + 2)(t + 3)

362 A study was designed to test the effectiveness of a new drug. Half of the volunteers received the drug. The other half received a sugar pill. The probability of a volunteer receiving the drug and getting well was 40%. What is the probability of a volunteer getting well, given that the volunteer received the drug?

363 Simon lost his library card and has an overdue library book. When the book was 5 days late, he owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was 21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book. Suppose the total amount Simon owes when the book is n days late can be determined by an arithmetic sequence. Determine a formula for a n , the nth term of this sequence. Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book is 60 days late.


68

364 The J& B candy company claims that 45% of the candies it produces are blue, 30% are brown, and 25% are yellow. Each bag holds 65 candies. A simulation was run 200 times, each of sample size 65, based on the premise that 45% of the candies are blue. The results of the simulation are shown below.

Bonnie purchased a bag of J& B's candy and counted 24 blue candies. What inference can be made regarding a bag of J& B's with only 24 blue candies?1) The company is not meeting their production

standard.2) Bonnie's bag was a rarity and the company

should not be concerned.3) The company should change their claim to 37%

blue candies are produced.4) Bonnie's bag is within the middle 95% of the

simulated data supporting the company's claim.

365 The speed of a tidal wave, s, in hundreds of miles per hour, can be modeled by the equation s = t − 2t + 6, where t represents the time from its origin in hours. Algebraically determine the time when s = 0. How much faster was the tidal wave traveling after 1 hour than 3 hours, to the nearest mile per hour? Justify your answer.

366 The expression m2

m13

−12

is equivalent to

1) − m56

2) 1

m56

3) −m m5

4) 1m m5

367 Determine if x − 5 is a factor of 2x3 − 4x2 − 7x − 10. Explain your answer.

368 The value of a new car depreciates over time. Greg purchased a new car in June 2011. The value, V, of his car after t years can be modeled by the equation

log0.8V

17000

= t . What is the average decreasing

rate of change per year of the value of the car from June 2012 to June 2014, to the nearest ten dollars per year?1) 19602) 21803) 24504) 2770

369 What is the completely factored form of k 4 − 4k 2 + 8k 3 − 32k + 12k 2 − 48?1) (k − 2)(k − 2)(k + 3)(k + 4)2) (k − 2)(k − 2)(k + 6)(k + 2)3) (k + 2)(k − 2)(k + 3)(k + 4)4) (k + 2)(k − 2)(k + 6)(k + 2)


69

370 Graph y = log2(x + 3) − 5 on the set of axes below. Use an appropriate scale to include both intercepts.

Describe the behavior of the given function as x approaches −3 and as x approaches positive infinity.

371 The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by

H(t) = 70sin 2π7 t − 1.75

+ 80, where t is time,

in minutes. Using H(t) for one full rotation, this car's minimum height, in feet, is1) 1502) 703) 104) 0

372 Write x3 • x as a single term with a rational exponent.

373 Given z x = 6x3 + bx 2 − 52x + 15, z 2 = 35, and z −5 = 0, algebraically determine all the zeros of z x .

374 If f(x) = 3 x| | − 1 and g(x) = 0.03x3 − x + 1, an approximate solution for the equation f(x) = g(x) is1) 1.962) 11.293) (−0.99,1.96)4) (11.29,32.87)

375 Consider the end behavior description below.• as x → −∞, f(x) → ∞• as x → ∞, f(x) → −∞Which function satisfies the given conditions?1) f(x) = x4 + 2x2 + 1

2)3) f(x) = −x3 + 2x − 6

4)

376 Write (5 + 2yi)(4 − 3i) − (5− 2yi)(4 − 3i) in a + bi form, where y is a real number.


70

377 Explain how 315

2

can be written as the

equivalent radical expression 95 .

378 The probability that Gary and Jane have a child with blue eyes is 0.25, and the probability that they have a child with blond hair is 0.5. The probability that they have a child with both blue eyes and blond hair is 0.125. Given this information, the events blue eyes and blond hair are I: dependent II: independent III: mutually exclusive1) I, only2) II, only3) I and III4) II and III

379 Given x ≠ −2, the expression 2x 2 + 5x + 8x + 2 is

equivalent to

1) 2x2 + 9x + 2

2) 2x + 7x + 2

3) 2x + 1 + 6x + 2

4) 2x + 9 − 10x + 2

380 If p(x) = ab x and r(x) = cdx , then p(x) • r(x) equals1) ac(b + d)x

2) ac(b + d)2x

3) ac(bd)x

4) ac(bd)x2

381 A manufacturing company has developed a cost model, C(x) = 0.15x3 + 0.01x 2 + 2x + 120, where x is the number of items sold, in thousands. The sales price can be modeled by S(x) = 30− 0.01x. Therefore, revenue is modeled by R(x) = x •S(x). The company's profit, P(x) = R(x) −C(x), could be modeled by1) 0.15x 3 + 0.02x2 − 28x + 1202) −0.15x3 − 0.02x2 + 28x − 1203) −0.15x3 + 0.01x2 − 2.01x − 1204) −0.15x 3 + 32x + 120

382 Algebraically determine whether the function j(x) = x4 − 3x 2 − 4 is odd, even, or neither.

383 A student studying public policy created a model for the population of Detroit, where the population decreased 25% over a decade. He used the model P = 714(0.75)d , where P is the population, in thousands, d decades after 2010. Another student, Suzanne, wants to use a model that would predict the population after y years. Suzanne's model is best represented by1) P = 714(0.6500) y

2) P = 714(0.8500) y

3) P = 714(0.9716) y

4) P = 714(0.9750) y

384 Given events A and B, such that P(A) = 0.6, P(B) = 0.5, and P(A∪B) = 0.8, determine whether A and B are independent or dependent.


71

385 Elaina has decided to run the Buffalo half-marathon in May. She researched training plans on the Internet and is looking at two possible plans: Jillian’s 12-week plan and Josh’s 14-week plan. The number of miles run per week for each plan is plotted below.

Which one of the plans follows an arithmetic pattern? Explain how you arrived at your answer. Write a recursive definition to represent the number of miles run each week for the duration of the plan you chose. Jillian’s plan has an alternative if Elaina wanted to train instead for a full 26-mile marathon. Week one would start at 13 miles and follow the same pattern for the half-marathon, but it would continue for 14 weeks. Write an explicit formula, in simplest form, to represent the number of miles run each week for the full-marathon training plan.

386 For x ≠ 0, which expressions are equivalent to one divided by the sixth root of x?

I. x6

x3 II. x16

x13

III. x−16

1) I and II, only2) I and III, only3) II and III, only4) I, II, and III

387 Consider the system shown below.2x − y = 4

(x + 3)2 + y2 = 8The two solutions of the system can be described as1) both imaginary2) both irrational3) both rational4) one rational and one irrational


72

388 Stephen’s Beverage Company is considering whether to produce a new brand of cola. The company will launch the product if at least 25% of cola drinkers will buy the product. Fifty cola drinkers are randomly selected to take a blind taste-test of products A, B, and the new product. Nine out of fifty participants preferred Stephen’s new cola to products A and B. The company then devised a simulation based on the requirement that 25% of cola drinkers will buy the product. Each dot in the graph shown below represents the proportion of people who preferred Stephen’s new product, each of sample size 50, simulated 100 times.

Assume the set of data is approximately normal and the company wants to be 95% confident of its results. Does the sample proportion obtained from the blind taste-test, nine out of fifty, fall within the margin of error developed from the simulation? Justify your answer. The company decides to continue developing the product even though only nine out of fifty participants preferred its brand of cola in the taste-test. Describe how the simulation data could be used to support this decision.

389 Which investigation technique is most often used to determine if a single variable has an impact on a given population?1) observational study2) random survey3) controlled experiment4) formal interview

390 What is the solution to 8(2x + 3 ) = 48?

1) x = ln6ln2 − 3

2) x = 0

3) x = ln48ln16 − 3

4) x = ln4− 3

391 The solution to the equation 18x2 − 24x + 87 = 0 is

1) −23 ± 6i 158

2) −23 ± 1

6 i 158

3) 23 ± 6i 158

4) 23 ± 1

6 i 158

392 Which equation has 1− i as a solution?1) x2 + 2x − 2 = 02) x2 + 2x + 2 = 03) x2 − 2x − 2 = 04) x2 − 2x + 2 = 0

393 Which statement about statistical analysis is false?1) Experiments can suggest patterns and

relationships in data.2) Experiments can determine cause and effect

relationships.3) Observational studies can determine cause and

effect relationships.4) Observational studies can suggest patterns and

relationships in data.


73

394 The graph below represents the height above the ground, h, in inches, of a point on a triathlete's bike wheel during a training ride in terms of time, t, in seconds.

Identify the period of the graph and describe what the period represents in this context.

395 The results of a poll of 200 students are shown in the table below:

Preferred Music StyleTechno Rap Country

Female 54 25 27Male 36 40 18

For this group of students, do these data suggest that gender and preferred music styles are independent of each other? Justify your answer.

396 Which statement regarding the graphs of the functions below is untrue?

f(x) = 3sin2x, from -π < x < π

g(x) = (x − 0.5)(x + 4)(x − 2)

h(x) = log2x

j(x) = −|4x − 2|+ 31) f(x) and j(x) have a maximum y-value of 3.2) f(x), h(x), and j(x) have one y-intercept.3) g(x) and j(x) have the same end behavior as

x → −∞ .4) g(x), h(x), and j(x) have rational zeros.

397 A public opinion poll was conducted on behalf of Mayor Ortega's reelection campaign shortly before the election. 264 out of 550 likely voters said they would vote for Mayor Ortega; the rest said they would vote for his opponent. Which statement is least appropriate to make, according to the results of the poll?1) There is a 48% chance that Mayor Ortega will

win the election.2) The point estimate (p) of voters who will vote

for Mayor Ortega is 48%.3) It is most likely that between 44% and 52% of

voters will vote for Mayor Ortega.4) Due to the margin of error, an inference cannot

be made regarding whether Mayor Ortega or his opponent is most likely to win the election.


74

398 A game spinner is divided into 6 equally sized regions, as shown in the diagram below.

For Miles to win, the spinner must land on the number 6. After spinning the spinner 10 times, and losing all 10 times, Miles complained that the spinner is unfair. At home, his dad ran 100 simulations of spinning the spinner 10 times,

assuming the probability of winning each spin is 16.

The output of the simulation is shown in the diagram below.

Which explanation is appropriate for Miles and his dad to make?1) The spinner was likely unfair, since the number

6 failed to occur in about 20% of the simulations.

2) The spinner was likely unfair, since the spinner should have landed on the number 6 by the sixth spin.

3) The spinner was likely not unfair, since the number 6 failed to occur in about 20% of the simulations.

4) The spinner was likely not unfair, since in the output the player wins once or twice in the majority of the simulations.

399 When g(x) is divided by x + 4, the remainder is 0. Given g(x) = x4 + 3x3 − 6x2 − 6x + 8, which conclusion about g(x) is true?1) g(4) = 02) g(−4) = 03) x − 4 is a factor of g(x).4) No conclusion can be made regarding g(x).

400 A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. The volume of the box is modeled by the function below.

Over which interval is the volume of the box changing at the fastest average rate?1) [1,2]2) [1,3.5]3) [1,5]4) [0,3.5]

401 The roots of the equation x2 + 2x + 5 = 0 are1) −3 and 12) −1, only3) −1 + 2i and − 1 − 2i4) −1 + 4i and − 1 − 4i


75

402 The expression 6xi3(−4xi + 5) is equivalent to1) 2x − 5i2) −24x2 − 30xi3) −24x2 + 30x − i4) 26x − 24x 2 i − 5i

403 A study of the annual population of the red-winged blackbird in Ft. Mill, South Carolina, shows the population, B(t), can be represented by the function B(t) = 750(1.16) t , where the t represents the number of years since the study began. In terms of the monthly rate of growth, the population of red-winged blackbirds can be best approximated by the function1) B(t) = 750(1.012) t

2) B(t) = 750(1.012)12t

3) B(t) = 750(1.16)12t

4) B(t) = 750(1.16)t

12

404 lridium-192 is an isotope of iridium and has a half-life of 73.83 days. If a laboratory experiment begins with 100 grams of Iridium-192, the number of grams, A, of Iridium-192 present after t days

would be A = 100 12

t73.83

. Which equation

approximates the amount of Iridium-192 present after t days?

1) A = 100 73.832

t

2) A = 100 1147.66

t

3) A = 100(0.990656) t

4) A = 100(0.116381) t

405 Julie averaged 85 on the first three tests of the semester in her mathematics class. If she scores 93 on each of the remaining tests, her average will be 90. Which equation could be used to determine how many tests, T, are left in the semester?

1) 255 + 93T3T = 90

2) 255 + 90T3T = 93

3) 255 + 93TT + 3 = 90

4) 255 + 90TT + 3 = 93

406 Mrs. Jones had hundreds of jelly beans in a bag that contained equal numbers of six different flavors. Her student randomly selected four jelly beans and they were all black licorice. Her student complained and said "What are the odds I got all of that kind?" Mrs. Jones replied, "simulate rolling a die 250 times and tell me if four black licorice jelly beans is unusual." Explain how this simulation could be used to solve the problem.

407 Sean's team has a baseball game tomorrow. He pitches 50% of the games. There is a 40% chance of rain during the game tomorrow. If the probability that it rains given that Sean pitches is 40%, it can be concluded that these two events are1) independent2) dependent3) mutually exclusive4) complements

408 Explain how (−8)43 can be evaluated using

properties of rational exponents to result in an integer answer.


76

409 The formula below can be used to model which scenario?

a 1 = 3000

an = 0.80an − 1

1) The first row of a stadium has 3000 seats, and each row thereafter has 80 more seats than the row in front of it.

2) The last row of a stadium has 3000 seats, and each row before it has 80 fewer seats than the row behind it.

3) A bank account starts with a deposit of $3000, and each year it grows by 80%.

4) The initial value of a specialty toy is $3000, and its value each of the following years is 20% less.

410 Sally’s high school is planning their spring musical. The revenue, R, generated can be determined by the function R(t) = −33t2 + 360t , where t represents the price of a ticket. The production cost, C, of the musical is represented by the function C(t) = 700+ 5t. What is the highest ticket price, to the nearest dollar, they can charge in order to not lose money on the event?1) t = 32) t = 53) t = 84) t = 11

411 Which statement regarding polynomials and their zeros is true?1) f(x) = (x 2 − 1)(x + a) has zeros of 1 and −a,

only.2) f(x) = x3 − ax 2 + 16x − 16a has zeros of 4 and

a, only.3) f(x) = (x2 + 25)(x + a) has zeros of ±5 and −a.4) f(x) = x3 − ax 2 − 9x + 9a has zeros of ±3 and a.

412 Describe the transformation applied to the graph of p(x) = 2x that forms the new function q(x) = 2x − 3 + 4.

413 On the grid below, sketch a cubic polynomial whose zeros are 1, 3, and -2.

414 Relative to the graph of y = 3sinx , what is the shift

of the graph of y = 3sin x + π3

?

1) π3 right

2) π3 left

3) π3 up

4) π3 down


77

415 Show why x − 3 is a factor of m(x) = x3 − x 2 − 5x − 3. Justify your answer.

416 Which situation best describes conditional probability?1) finding the probability of an event occurring

two or more times2) finding the probability of an event occurring

only once3) finding the probability of two independent

events occurring at the same time4) finding the probability of an event occurring

given another event had already occurred

417 Kristin wants to increase her running endurance. According to experts, a gradual mileage increase of 10% per week can reduce the risk of injury. If Kristin runs 8 miles in week one, which expression can help her find the total number of miles she will have run over the course of her 6-week training program?

1) 8(1.10)n − 1

n = 1

6

∑

2) 8(1.10)n

n = 1

6

∑

3)8− 8(1.10)6

0.90

4)8− 8(0.10)n

1.10

418 Which equation represents a parabola with the focus at (0,−1) and the directrix of y = 1?1) x 2 = −8y2) x 2 = −4y3) x 2 = 8y4) x 2 = 4y

419 The lifespan of a 60-watt lightbulb produced by a company is normally distributed with a mean of 1450 hours and a standard deviation of 8.5 hours. If a 60-watt lightbulb produced by this company is selected at random, what is the probability that its lifespan will be between 1440 and 1465 hours?1) 0.38032) 0.46123) 0.84154) 0.9612

420 Which expression is equivalent to 4x3 + 9x − 52x − 1 ,

where x ≠ 12 ?

1) 2x2 + x + 5

2) 2x2 + 112 + 1

2(2x − 1)3) 2x2 − x + 5

4) 2x2 − x + 4 + 12x − 1

421 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponential growth, approximate the annual growth rate, to the nearest percent.

422 The eighth and tenth terms of a sequence are 64 and 100. If the sequence is either arithmetic or geometric, the ninth term can not be1) −822) −803) 804) 82

423 Express 1− i 3 in a + bi form.


78

424 The distribution of the diameters of ball bearings made under a given manufacturing process is normally distributed with a mean of 4 cm and a standard deviation of 0.2 cm. What proportion of the ball bearings will have a diameter less than 3.7 cm?1) 0.06682) 0.43323) 0.86644) 0.9500

425 The completely factored form of 2d 4 + 6d 3 − 18d 2 − 54d is1) 2d(d 2 − 9)(d + 3)2) 2d(d 2 + 9)(d + 3)3) 2d(d + 3)2(d − 3)4) 2d(d − 3)2(d + 3)

426 Which equation represents a parabola with a focus of (0,4) and a directrix of y = 2?1) y = x2 + 32) y = −x 2 + 1

3) y = x2

2 + 3

4) y = x2

4 + 3

427 Given f(x) = 3x2 + 7x − 20 and g(x) = x − 2, state

the quotient and remainder of f(x)g(x) , in the form

q(x) +r(x)g(x) .

428 Anne has a coin. She does not know if it is a fair coin. She flipped the coin 100 times and obtained 73 heads and 27 tails. She ran a computer simulation of 200 samples of 100 fair coin flips. The output of the proportion of heads is shown below.

Given the results of her coin flips and of her computer simulation, which statement is most accurate?1) 73 of the computer's next 100 coin flips will be

heads.2) 50 of her next 100 coin flips will be heads.3) Her coin is not fair.4) Her coin is fair.

429 Which expression is not a solution to the equation 2t = 10?

1) 12 log2 10

2) log2 103) log4104) log104

430 Which value, to the nearest tenth, is not a solution of p(x) = q(x) if p(x) = x 3 + 3x2 − 3x − 1 and q(x) = 3x + 8?1) −3.92) −1.13) 2.14) 4.7


79

431 Which graph has the following characteristics?• three real zeros• as x → −∞, f(x) → −∞• as x → ∞, f(x) → ∞

1)

2)

3)

4)

432 Use the properties of rational exponents to determine the value of y for the equation:

x83

x4

13

= x y, x > 1

433 Which scenario is best described as an observational study?1) For a class project, students in Health class ask

every tenth student entering the school if they eat breakfast in the morning.

2) A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts.

3) A researcher wants to learn whether or not there is a link between children's daily amount of physical activity and their overall energy level. During lunch at the local high school, she distributed a short questionnaire to students in the cafeteria.

4) Sixty seniors taking a course in Advanced Algebra Concepts are randomly divided into two classes. One class uses a graphing calculator all the time, and the other class never uses graphing calculators. A guidance counselor wants to determine whether there is a link between graphing calculator use and students' final exam grades.

434 Which expression has been rewritten correctly to form a true statement?1) (x + 2)2 + 2(x + 2) − 8 = (x + 6)x2) x4 + 4x2 + 9x2y2 − 36y2 = (x + 3y)2 (x − 2)2

3) x3 + 3x2 − 4xy2 − 12y2 = (x − 2y)(x + 3)2

4) (x 2 − 4)2 − 5(x 2 − 4) − 6 = (x2 − 7)(x 2 − 6)

435 A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and P(t) is the population of rabbits with respect to time, about how many rabbits will there be in 98 days?1) 562) 1523) 36884) 81,920


80

436 Using a microscope, a researcher observed and recorded the number of bacteria spores on a large sample of uniformly sized pieces of meat kept at room temperature. A summary of the data she recorded is shown in the table below.

Hours (x) Average Numberof Spores (y)

0 40.5 101 152 603 2604 11306 16,380

Using these data, write an exponential regression equation, rounding all values to the nearest thousandth. The researcher knows that people are likely to suffer from food-borne illness if the number of spores exceeds 100. Using the exponential regression equation, determine the maximum amount of time, to the nearest quarter hour, that the meat can be kept at room temperature safely.

437 The set of data in the table below shows the results of a survey on the number of messages that people of different ages text on their cell phones each month.

Text Messages per MonthAge Group 0-10 11-50 Over 50

15-18 4 37 6819-22 6 25 8723-60 25 47 157

If a person from this survey is selected at random, what is the probability that the person texts over 50 messages per month given that the person is between the ages of 23 and 60?

1) 157229 3) 157

384

2) 157312 4) 157

456

438 Verify the following Pythagorean identity for all values of x and y:(x2 + y2 )2 = (x 2 − y2 )2 + (2xy)2


81

439 The x-value of which function’s x-intercept is larger, f or h? Justify your answer.

f(x) = log(x − 4)

x h(x)−1 60 41 22 03 −2

440 The function M(t) represents the mass of radium over time, t, in years.

M(t) = 100e

ln12

t

1590

Determine if the function M(t) represents growth or decay. Explain your reasoning.

441 The volume of air in a person’s lungs, as the person breathes in and out, can be modeled by a sine graph. A scientist is studying the differences in this volume for people at rest compared to people told to take a deep breath. When examining the graphs, should the scientist focus on the amplitude, period, or midline? Explain your choice.

442 The solution set for the equation x + 14 − 2x + 5 = 1 is

1) {−6}2) {2}3) {18}4) {2,22}

443 Graph y = 400(.85)2x − 6 on the set of axes below.

444 In 2013, approximately 1.6 million students took the Critical Reading portion of the SAT exam. The mean score, the modal score, and the standard deviation were calculated to be 496, 430, and 115, respectively. Which interval reflects 95% of the Critical Reading scores?1) 430± 1152) 430± 2303) 496± 1154) 496± 230


82

445 The value of a certain small passenger car based on its use in years is modeled by V(t) = 28482.698(0.684) t , where V(t) is the value in dollars and t is the time in years. Zach had to take out a loan to purchase the small passenger car. The function Z(t) = 22151.327(0.778) t , where Z(t) is measured in dollars, and t is the time in years, models the unpaid amount of Zach's loan over time. Graph V(t) and Z(t) over the interval 0 ≤ t ≤ 5, on the set of axes below.

State when V(t) = Z(t), to the nearest hundredth, and interpret its meaning in the context of the problem. Zach takes out an insurance policy that requires him to pay a $3000 deductible in case of a collision. Zach will cancel the collision policy when the value of his car equals his deductible. To the nearest year, how long will it take Zach to cancel this policy? Justify your answer.

446 Algebraically determine the values of h and k to correctly complete the identity stated below.

2x3 − 10x 2 + 11x − 7 = (x − 4)(2x2 + hx + 3) + k

447 Which expression is equivalent to (3k − 2i)2 , where i is the imaginary unit?1) 9k 2 − 42) 9k 2 + 43) 9k 2 − 12ki − 44) 9k 2 − 12ki + 4

448 What is the solution to the system of equations y = 3x − 2 and y = g(x) where g(x) is defined by the function below?

1) {(0,−2)}2) {(0,−2),(1,6)}3) {(1,6)}4) {(1,1),(6,16)}

449 As θ increases from −π2 to 0 radians, the value of

cosθ will1) decrease from 1 to 02) decrease from 0 to −13) increase from −1 to 04) increase from 0 to 1


83

450 Given that sin2θ + cos2θ = 1 and sinθ = − 25 ,

what is a possible value of cosθ ?

1)5+ 2

5

2)235

3)3 3

5

4)355

451 Consider the system below.

x + y + z = 9

x − y − z = −1

x − y + z = 21

Which value is not in the solution, (x,y,z), of the system?1) −82) −63) 114) 4

452 The expression −3x2 − 5x + 2x 3 + 2x2 can be rewritten as

1) −3x − 3x2 + 2x

2) −3x − 1x2

3) −3x−1 + 14) −3x−1 + x−2

453 a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline at

y = −32 , and a period of 2π .

b) Explain any differences between a sketch of

y = 2sin x − π3

−32 and the sketch from part a.

454 Seth’s parents gave him $5000 to invest for his 16th birthday. He is considering two investment options. Option A will pay him 4.5% interest compounded annually. Option B will pay him 4.6% compounded quarterly. Write a function of option A and option B that calculates the value of each account after n years. Seth plans to use the money after he graduates from college in 6 years. Determine how much more money option B will earn than option A to the nearest cent. Algebraically determine, to the nearest tenth of a year, how long it would take for option B to double Seth’s initial investment.


84

455 Gabriel performed an experiment to see if planting 13 tomato plants in black plastic mulch leads to larger tomatoes than if 13 plants are planted without mulch. He observed that the average weight of the tomatoes from tomato plants grown in black plastic mulch was 5 ounces greater than those from the plants planted without mulch. To determine if the observed difference is statistically significant, he rerandomized the tomato groups 100 times to study these random differences in the mean weights. The output of his simulation is summarized in the dotplot below.

Given these results, what is an appropriate inference that can be drawn?1) There was no effect observed between

the two groups.3) There is strong evidence to support the

hypothesis that tomatoes from plants planted in black plastic mulch are larger than those planted without mulch.

2) There was an effect observed that could be due to the random assignment of plants to the groups.

4) There is strong evidence to support the hypothesis that tomatoes from plants planted without mulch are larger than those planted in black plastic mulch.

456 A ball is dropped from a height of 32 feet. It bounces and rebounds 80% of the height from which it was falling. What is the total downward distance, in feet, the ball traveled up to the 12th bounce?1) 292) 583) 1204) 149

457 Algebraically determine the values of x that satisfy the system of equations below.

y = −2x + 1

y = −2x 2 + 3x + 1

458 As x increases from 0 to π2 , the graph of the

equation y = 2tanx will1) increase from 0 to 22) decrease from 0 to −23) increase without limit4) decrease without limit

459 The zeros for f(x) = x4 − 4x3 − 9x2 + 36x are1) {0,±3,4}2) {0,3,4}3) {0,±3,−4}4) {0,3,−4}


85

460 The ocean tides near Carter Beach follow a repeating pattern over time, with the amount of time between each low and high tide remaining relatively constant. On a certain day, low tide occurred at 8:30 a.m. and high tide occurred at 3:00 p.m. At high tide, the water level was 12 inches above the average local sea level; at low tide it was 12 inches below the average local sea level. Assume that high tide and low tide are the maximum and minimum water levels each day, respectively. Write a cosine function of the form f(t) = A cos(Bt), where A and B are real numbers, that models the water level, f(t), in inches above or below the average Carter Beach sea level, as a function of the time measured in t hours since 8:30 a.m. On the grid below, graph one cycle of this function.

People who fish in Carter Beach know that a certain species of fish is most plentiful when the water level is increasing. Explain whether you would recommend fishing for this species at 7:30 p.m. or 10:30 p.m. using evidence from the given context.

461 Graph y = x3 − 4x2 + 2x + 7 on the set of axes below.

462 Two versions of a standardized test are given, an April version and a May version. The statistics for the April version show a mean score of 480 and a standard deviation of 24. The statistics for the May version show a mean score of 510 and a standard deviation of 20. Assume the scores are normally distributed. Joanne took the April version and scored in the interval 510-540. What is the probability, to the nearest ten thousandth, that a test paper selected at random from the April version scored in the same interval? Maria took the May version. In what interval must Maria score to claim she scored as well as Joanne?

463 Solve algebraically for all values of x: x − 4 + x = 6


86

464 Which function shown below has a greater average rate of change on the interval [−2,4]? Justify your answer.

x f(x)−4 0.3125−3 0.625−2 1.25−1 2.50 51 102 203 404 805 1606 320

g(x) = 4x3 − 5x2 + 3

465 Mr. Farison gave his class the three mathematical rules shown below to either prove or disprove. Which rules can be proved for all real numbers?

I (m+ p)2 = m2 + 2mp + p 2

II (x + y)3 = x3 + 3xy + y 3

III (a 2 + b 2)2 = (a 2 − b 2 )2 + (2ab)2

1) I, only2) I and II3) II and III4) I and III

466 Which value is not contained in the solution of the system shown below?

a + 5b − c = −20

4a − 5b + 4c = 19

−a − 5b − 5c = 21) −22) 23) 34) −3

467 The expression 81x8 y64 is equivalent to

1) 3x2 y32

2) 3x4y2

3) 9x2 y32

4) 9x4y2

468 The expression (x + a)2 + 5(x + a) + 4 is equivalent to1) (a + 1)(a + 4)2) (x + 1)(x + 4)3) (x + a + 1)(x + a + 4)4) x 2 + a 2 + 5x + 5a + 4

469 Algebraically prove that the difference of the squares of any two consecutive integers is an odd integer.


87

470 A circle centered at the origin has a radius of 10 units. The terminal side of an angle, θ , intercepts the circle in Quadrant II at point C. The y-coordinate of point C is 8. What is the value of cosθ ?

1) −35

2) −34

3) 35

4) 45

471 A payday loan company makes loans between $100 and $1000 available to customers. Every 14 days, customers are charged 30% interest with compounding. In 2013, Remi took out a $300 payday loan. Which expression can be used to calculate the amount she would owe, in dollars, after one year if she did not make payments?

1) 300(.30)14365

2) 300(1.30)14365

3) 300(.30)36514

4) 300(1.30)36514

472 Which statement is incorrect for the graph of the

function y = −3cos π3 x − 4

+ 7?

1) The period is 6.2) The amplitude is 3.3) The range is [4,10].4) The midline is y = −4.

473 Which binomial is not a factor of the expression x3 − 11x2 + 16x + 84?1) x + 22) x + 43) x − 64) x − 7

474 Which graph represents a cosine function with no horizontal shift, an amplitude of 2, and a period of 2π3 ?

1)

2)

3)

4)


88

475 The Rickerts decided to set up an account for their daughter to pay for her college education. The day their daughter was born, they deposited $1000 in an account that pays 1.8% compounded annually. Beginning with her first birthday, they deposit an additional $750 into the account on each of her birthdays. Which expression correctly represents the amount of money in the account n years after their daughter was born?1) an = 1000(1.018)n + 7502) an = 1000(1.018)n + 750n3) a 0 = 1000

an = an − 1 (1.018) + 7504) a 0 = 1000

an = an − 1 (1.018) + 750n

ID: A

1

Algebra II Regents at RandomAnswer Section

1 ANS:

The period of P is 23, which means the patient’s blood pressure reaches a high every 2

3

second and a low every 23 second. The patient’s blood pressure is high because 144 over 96 is greater than 120

over 80.

PTS: 6 REF: 011837aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: graph

2 ANS: 4(1) quadratic has two roots and both are real (−2,0) and (−0.5,0), (2) x = ± 32 − 3, (3) the real root is 3, with a multiplicity of 2, (4) x = ±4i

PTS: 2 REF: 011909aii NAT: A.REI.B.4 TOP: Using the DiscriminantKEY: determine nature of roots given equation, graph, table

3 ANS: 2 PTS: 2 REF: 011901aii NAT: S.ID.A.4TOP: Normal Distributions KEY: mean and standard deviation

4 ANS: 3

y = 278(0.5)181.8 ≈ 0.271

PTS: 2 REF: 011920aii NAT: F.LE.A.2 TOP: Modeling Exponential Functions 5 ANS: 4

1 year = 365 days

PTS: 2 REF: 061823aii NAT: A.SSE.B.3 TOP: Modeling Exponential Functions 6 ANS:

1200 ⋅ 0.784 ≈ 941

PTS: 2 REF: 081828aii NAT: S.ID.A.4 TOP: Normal DistributionsKEY: predict

7 ANS: 2 PTS: 2 REF: 061802aii NAT: F.IF.C.7TOP: Graphing Exponential Functions

ID: A

2

8 ANS: 3

x =−2 ± 22 − 4(3)(7)

2(3) =−2 ± −80

6 =−2 ± i 16 5

6 = −13 ±

2i 53

PTS: 2 REF: 081809aii NAT: A.REI.B.4 TOP: Solving QuadraticsKEY: complex solutions | quadratic formula

9 ANS: 16 − (3x − 2i)(3x − 2i) = 6− 9x2 − 12xi + 4i2

= 6 − 9x2 + 12xi + 4 = −9x2 + 12xi + 10

PTS: 2 REF: 061915aii NAT: N.CN.A.2 TOP: Operations with Complex Numbers 10 ANS: 1

x(x2 − 9)−(x2 − 9)

= −x

PTS: 2 REF: 012023aii NAT: A.APR.D.6 TOP: Rational ExpressionsKEY: factoring

11 ANS:

M =

(152500 − 15250) .03612

1+ .03612

360

1+ .03612

360

− 1≈ 624

PTS: 2 REF: 061831aii NAT: A.SSE.B.4 TOP: Series 12 ANS: 2

2− x − 1x + 2

1+ x + 2x + 2 − x − 1

x + 2

1 +x + 2 − (x − 1)

x + 2

1+ 3x + 2

PTS: 2 REF: 081907aii NAT: A.APR.D.7 TOP: Addition and Subtraction of Rationals 13 ANS:

96 = 1.5 a 1 = 6

an = 1.5 ⋅ an − 1

PTS: 2 REF: 061931aii NAT: F.LE.A.2 TOP: SequencesKEY: recursive

ID: A

3

14 ANS: 3

x2 (x + 2) − 9(x + 2)

x x 2 − x − 6

=x 2 − 9

(x + 2)

x(x − 3)(x + 2) =(x + 3)(x − 3)

x(x − 3) = x + 3x


15 ANS: 1−1216 = 9

−12 = −6.759

PTS: 2 REF: 012017aii NAT: F.IF.A.3 TOP: SequencesKEY: difference or ratio

16 ANS: 1The time of the next high tide will be the midpoint of consecutive low tides.

PTS: 2 REF: 011907aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: mixed

17 ANS: y = 101.523(.883)x 29 = 101.523(.883)x

29101.523 = (.883)x

log 29101.523 = x log(.883)

log 29101.523

log(.883) = x

x ≈ 10.07

PTS: 4 REF: 012036aii NAT: S.ID.B.6 TOP: RegressionKEY: exponential

18 ANS: 3440× 2.3% ≈ 10


19 ANS:

S 10 =15 − 15(1.03)10

1− 1.03 ≈ 171.958

PTS: 2 REF: 011929aii NAT: A.SSE.B.4 TOP: Series

ID: A

4

20 ANS: 42x = 4x

x + 3

2x + 6 = 4x 2

4x2 − 2x − 6 = 0

2 2x 2 − x − 3

= 0

(2x − 3)(x + 1) = 0

x = 32 ,−1

PTS: 2 REF: 061809aii NAT: A.REI.A.2 TOP: Solving Rationals 21 ANS:

−6(x + 3) −3x + 3 − x

6 + 1 = 0

18 + x(x + 3) − 6(x + 3) = 0

18+ x2 + 3x − 6x − 18 = 0

x2 − 3x = 0

x(x − 3) = 0

x = 0,3

PTS: 2 REF: 081829aii NAT: A.REI.A.2 TOP: Solving RationalsKEY: rational solutions

22 ANS: 47108 = 1

4 + 116459 − P(M and J)

P(M and J) = 31459

; No, because 31459 ≠ 1

4 ⋅ 116459

PTS: 4 REF: 011834aii NAT: S.CP.A.3 TOP: Conditional Probability 23 ANS:

a 1 = 3 a 2 = 7 a 3 = 15 a 4 = 31; No, because there is no common ratio: 73 ≠ 15

7

PTS: 2 REF: 061830aii NAT: F.IF.A.3 TOP: SequencesKEY: recursive

ID: A

5

24 ANS:

t2 + 47

2

= 1

t2 + 1649 = 49

49

t2 = 3349

t =± 33

7

−337

PTS: 2 REF: 011931aii NAT: F.TF.A.2 TOP: Unit Circle 25 ANS:

2x32

2x22

= x12 = x

PTS: 2 REF: 081826aii NAT: N.RN.A.2 TOP: Radicals and Rational ExponentsKEY: variables

26 ANS: i2 = −1, and not 1; 10+ 10i


(x + 7)(x − 1) = x2 + 6x − 7 = x2 + 6x + 9− 7− 9 = (x + 3)2 − 16

PTS: 2 REF: 061808aii NAT: A.APR.C.4 TOP: Polynomial Identities 28 ANS: 2 PTS: 2 REF: 061917aii NAT: F.LE.B.5

TOP: Modeling Exponential Functions 29 ANS:

an = 100(.8)n − 1 S 20 =100 − 100(.8)20

1 −.8 ≈ 494 No, because 494 > 40 × 12.


− 1− −34

2

= − 1616 − 9

16 = − 716 = −

74

PTS: 2 REF: 081905aii NAT: F.TF.C.8 TOP: Determining Trigonometric Functions

ID: A

6

31 ANS: 23− 18 = 5, x ± 2σ = −3.07 − 3.13, Yes, a difference of 5 or more occurred three times out of a thousand, which is statistically significant.

PTS: 4 REF: 061834aii NAT: S.IC.B.5 TOP: Analysis of Data 32 ANS: 1

1240(1.06)x = 890(1.11)x

x ≈ 7

PTS: 2 REF: 061814aii NAT: A.REI.D.11 TOP: Other Systems 33 ANS:

f(x) = x2 (x + 4)(x − 3); g(x) = (x + 2)2 (x + 6)(x − 1)

PTS: 4 REF: 011836aii NAT: A.APR.B.3 TOP: Graphing Polynomial Functions 34 ANS:

p(x)x − 1 = x2 + 7 + 5

x − 1

p(x) = x3 − x2 + 7x − 7 + 5

p(x) = x3 − x2 + 7x − 2

PTS: 2 REF: 061930aii NAT: A.APR.D.6 TOP: Rational ExpressionsKEY: division

35 ANS: 3(x + 3i)2 − (2x − 3i)2 = x2 + 6xi + 9i2 − 4x2 − 12xi + 9i2

= −3x 2 + 18xi


1.0064312 ≈ 1.08


2 = e0.0375t

t ≈ 18.5

PTS: 4 REF: 081835aii NAT: F.LE.A.4 TOP: Exponential Growth 38 ANS:

0.301 ± 2(0.058) → 0.185− 0.417 1460 ≈ 0.23. It is not unusual because 0.23 falls within this interval.

PTS: 4 REF: 081935aii NAT: S.IC.B.5 TOP: Analysis of Data

ID: A

7

39 ANS: 2

P = 2ππ45

= 90

PTS: 2 REF: 081822aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: period

40 ANS: 1 PTS: 2 REF: 011902aii NAT: F.IF.C.7TOP: Graphing Logarithmic Functions

41 ANS: 3y = x 3 − 2

x = y3 − 2

x + 2 = y 3

x + 23 = y

PTS: 2 REF: 061815aii NAT: F.BF.B.4 TOP: Inverse of FunctionsKEY: other

42 ANS: 3 PTS: 2 REF: 081819aii NAT: A.REI.D.11TOP: Other Systems

43 ANS: 6 − 2x + x = 2x + 30− 9

6 − 2x = x + 21

6− 2x = x 2 + 42x + 441

x 2 + 44x + 435 = 0

(x + 29)(x + 15) = 0

x = −29,−15

6− 2(−29) ≠ −29 + 21

64 ≠ −8

, so −29 is extraneous.

PTS: 4 REF: 061833aii NAT: A.REI.A.2 TOP: Solving RadicalsKEY: extraneous solutions

44 ANS: 20.254 ± 2(0.060) → (0.134,0.374)

PTS: 2 REF: 061913aii NAT: S.IC.B.5 TOP: Analysis of Data 45 ANS: 2 PTS: 2 REF: 011820aii NAT: S.IC.A.2

TOP: Analysis of Data 46 ANS: 4 PTS: 2 REF: 081906aii NAT: S.IC.B.3

TOP: Analysis of Data KEY: type

ID: A

8

47 ANS: 3x2 + (2x)2 = 5

x 2 + 4x 2 = 5

5x 2 = 5

x = ±1

y = 2x = ±2

PTS: 2 REF: 081916aii NAT: A.REI.C.7 TOP: Quadratic-Linear Systems 48 ANS:

x =−5 ± 52 + 4(2)(8)

2(2) = −54 ±

i 394


49 ANS: 2x = −6(y − 2)

−x6 = y − 2

−x6 + 2 = y

PTS: 2 REF: 011821aii NAT: F.BF.B.4 TOP: Inverse of FunctionsKEY: linear

50 ANS: 2

If cosθ = 725, sinθ = ±24

25, and tanθ = sinθcosθ =

−2425725

= −247

PTS: 2 REF: 081811aii NAT: F.TF.C.8 TOP: Determining Trigonometric Functions 51 ANS: 1 PTS: 2 REF: 011815aii NAT: F.TF.A.2

TOP: Unit Circle 52 ANS: 1

p(x) = r(x) − c(x)

−0.5x2 + 250x − 300 = −0.3x2 + 150x − c(x)

c(x) = 0.2x2 − 100x + 300

PTS: 2 REF: 061813aii NAT: F.BF.A.1 TOP: Operations with Functions

ID: A

9

53 ANS: 2f(x) = f(−x)

x 2 − 4 = (−x)2 − 4

x2 − 4 = x 2 − 4

PTS: 2 REF: 061806aii NAT: F.BF.B.3 TOP: Even and Odd Functions 54 ANS: 3

1.04112 ≈ 1.0032737


The denominator of the rational exponent represents the index of a root, and the 4th root of 81 is 3 and 33 is 27.

PTS: 2 REF: 011832aii NAT: N.RN.A.1 TOP: Radicals and Rational Exponents 56 ANS:

D = 1.223(2.652) A


57 ANS: 4 PTS: 2 REF: 081824aii NAT: S.CP.A.3TOP: Conditional Probability

58 ANS: 2 PTS: 2 REF: 011804aii NAT: F.TF.A.2TOP: Determining Trigonometric Functions KEY: radians

59 ANS:

tanθ = sinθcosθ =

−725

−2425

cosθ = −2425

PTS: 2 REF: 061928aii NAT: F.TF.C.8 TOP: Determining Trigonometric Functions 60 ANS: 2 PTS: 2 REF: 011910aii NAT: S.IC.B.3

TOP: Analysis of Data KEY: bias 61 ANS: 4 PTS: 2 REF: 081803aii NAT: F.BF.A.1

TOP: Operations with Functions 62 ANS: 4

log2(x − 1) − 1 = 0

log2 (x − 1) = 1

x − 1 = 21

x = 3

PTS: 2 REF: 061819aii NAT: F.IF.C.7 TOP: Graphing Logarithmic Functions 63 ANS: 1 PTS: 2 REF: 081813aii NAT: A.SSE.B.4

TOP: Series

ID: A

10

64 ANS: 4

1.06152

PTS: 2 REF: 061924aii NAT: F.BF.A.1 TOP: Modeling Exponential Functions 65 ANS: 2

4x • x23 + 2x

53 = 4x

53 + 2x

53 = 6x

53 = 6 x53

PTS: 2 REF: 061820aii NAT: N.RN.A.2 TOP: Operations with RadicalsKEY: with variables, index > 2

66 ANS: The denominator of the rational exponent represents the index of a root, and the numerator of the rational

exponent represents the power of the base. 9

5= 243

PTS: 2 REF: 081926aii NAT: N.RN.A.1 TOP: Radicals and Rational Exponents 67 ANS: 3

8r3 = 216

r3 = 27

r = 3

S 12 =8− 8(3)12

1 − 3 = 2125760


5+ 92 = 7, vertex: (−2,7); p = 7− 9 = −2, y = 1

4(−2) (x + 2)2 + 7

y − 7 = 1−8 (x + 2)2

−8(y − 7) = (x + 2)2

PTS: 2 REF: 061821aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions

ID: A

11

69 ANS: 4

2x − 1 10x3 − 3x2 − 7x + 35x2 + x − 3

10x3 − 5x2

2x 2 − 7x

2x 2 − x

− 6x + 3

−6x + 3



71 ANS: 1The cosine function has been translated +3. Since the maximum is 5 and the minimum is 1, the amplitude is 2. π3 = 2π

b

b = 6

.

PTS: 2 REF: 011913aii NAT: F.TF.B.5 TOP: Modeling Trigonometric Functions 72 ANS:

j(−1) = 2(−1)4 − (−1)3 − 35(−1)2 + 16(−1) + 48 = 2+ 1 − 35 − 16 + 48 = 0; x + 1 is a factor of j(x); 2x3 − 3x2 − 32x + 48 = 0

x2 (2x − 3) − 16(2x − 3) = 0

x2 − 16

(2x − 3) = 0

x = ±4, 32

PTS: 4 REF: 081834aii NAT: A.APR.B.2 TOP: Remainder Theorem 73 ANS: 1

(2x − i)2 − (2x − i)(2x + 3i)

(2x − i)[(2x − i) − (2x + 3i)]

(2x − i)(−4i)

−8xi + 4i2

−8xi − 4

PTS: 2 REF: 011911aii NAT: N.CN.A.2 TOP: Operations with Complex Numbers

ID: A

12

74 ANS:

16x4 − 81 = 4x2 + 9

4x 2 − 9

= 4x2 + 9

(2x + 3)(2x − 3). No, because ±3i

2 are roots.

PTS: 4 REF: 061933aii NAT: F.IF.B.4 TOP: Graphing Polynomial Functions 75 ANS: 2

y = 12 x + 8 x = 1

2 y + 8

2x = y + 16

y = 2x − 16


76 ANS: 3 PTS: 2 REF: 011917aii NAT: F.BF.B.4TOP: Inverse of Functions KEY: other

77 ANS: 4(x − y)2 = x2 − 2xy + y 2 (x + y)3 = x3 + 3x2 y + 3xy2 + y3

PTS: 2 REF: 061902aii NAT: A.APR.C.4 TOP: Polynomial Identities 78 ANS: 4

nm =

a 5

a = a52

a22

= a32 = a 3


79 ANS: 2

121(b)2 = 64

b = 811

64 811

2

≈ 34

PTS: 2 REF: 011904aii NAT: F.IF.A.3 TOP: SequencesKEY: explicit

80 ANS: 2 PTS: 2 REF: 011806aii NAT: A.APR.C.4TOP: Polynomial Identities

81 ANS: 1 PTS: 2 REF: 061904aii NAT: F.IF.B.6TOP: Rate of Change

ID: A

13

82 ANS:

3a − 2 6a 3 + 11a 2 − 4a − 9

6a 3 − 4a 2

15a 2 − 4a

15a 2 − 10a

6a − 9

6a − 4

− 5

2a 2 + 5a + 2 2a 2 + 5a + 2− 5

3a − 2


83 ANS:

PTS: 2 REF: 011932aii NAT: F.IF.C.7 TOP: Graphing Logarithmic Functions 84 ANS: 3

x23 • x

52

x16

= x46 • x

156

x16

= x186 = x3


85 ANS: 2b 2 = 2b 2 − 64

−b 2 = −64

b = ±8

−8 is extraneous.


ID: A

14

86 ANS: 1

1.025112 ≈ 1.00206


2x 2 + x − 3

• (x − 1) − 2x2 + x − 3

+ (x − 1)

2x 3 − 2x 2 + x2 − x − 3x + 3

− 2x2 + 2x − 4

2x3 − 3x2 − 6x + 7

PTS: 4 REF: 011833aii NAT: F.BF.A.1 TOP: Operations with Functions 88 ANS: 3

PTS: 2 REF: 011817aii NAT: F.IF.B.4 TOP: Graphing Polynomial Functions 89 ANS:

PTS: 2 REF: 061826aii NAT: F.IF.C.7 TOP: Graphing Polynomial Functions

ID: A

15

90 ANS: 3x2 − 4x − 5 = 4x 2 − 40x + 100

3x2 − 36x + 105 = 0

x2 − 12x + 35 = 0

(x − 7)(x − 5) = 0

x = 5,7


91 ANS: 4 PTS: 2 REF: 081810aii NAT: F.BF.A.2TOP: Sequences

92 ANS: 3

PTS: 2 REF: 081922aii NAT: F.IF.B.6 TOP: Rate of Change 93 ANS:

B(11) −B(8)11 − 8 ≈ −10.1 The average monthly high temperature decreases 10.1º each month from August to

November.


P(16) = log(16 − 4) ≈ 1.1, , 14000

PTS: 6 REF: 061837aii NAT: A.REI.D.11 TOP: Other Systems

ID: A

16

95 ANS: 4x2 − 4x

2x =x(x − 4)

2x = x − 42 = x

2 − 2 x − 12 − 3

2 = x − 1 − 32 = x − 4

2


96 ANS: 4p(5) = 2(5)3 − 3(5) + 5 = 240


400 ⋅.954 ≈ 380


98 ANS: 4

The maximum of p is 5. The minimum of f is −214 (x = −6

2(4) = −34

f −34

= 4 −34

2

+ 6 −34

− 3 = 4 916

−184 − 12

4 = −214 ). 20

4 − −214

=414 = 10.25

PTS: 2 REF: 011922aii NAT: F.IF.C.9 TOP: Comparing Functions 99 ANS: 3

−3 + 5i − 4 + 24i − 2i − 12i2

= −3 + 5i − (16+ 22i) = −19 − 17i


13 − k(1)2 + 2(1) = 0

k = 3


m3 − 2m2 + 4m− 8 = 0

m2 (m− 2) + 4(m− 2) = 0

m2 + 4

(m− 2) = 0

PTS: 2 REF: 081821aii NAT: A.APR.B.3 TOP: Solving Polynomial Equations 102 ANS: 1

N(10) −N(1)10 − 1 ≈ −2.03,

N(20) −N(10)20 − 10 ≈ −1.63,

N(25) −N(15)25 − 15 ≈ −1.46,

N(30) −N(1)30 − 1 ≈ −1.64

PTS: 2 REF: 061807aii NAT: F.IF.B.6 TOP: Rate of Change

ID: A

17

103 ANS: 2 PTS: 2 REF: 081911aii NAT: F.BF.B.3TOP: Even and Odd Functions

104 ANS: 4There is no x-intercept.

PTS: 2 REF: 011823aii NAT: F.IF.C.7 TOP: Graphing Exponential Functions 105 ANS:

Domain: x < 2, Asymptote x = 2


3x2y • 27x3y23 = 312 xy

12 •3

22 xy

23 = 3

32 x2 y

76


107 ANS:

y = −x + 1

(x − 2)2 + (−x + 1 − 3)2 = 16

x2 − 4x + 4+ x2 + 4x + 4 = 16

2x2 = 8

x = −2,2

y = −2 + 1 = −1 (2,−1)

y = 2 + 1 = 3 (−2,3)


−12 i3 3i − 4 − 3i2 = −3

2 i4 + 2i3 − 3i2 = −32 − 2i + 3 = 3

2 − 2i


ID: A

18

109 ANS: 4a 1 = 2.5 + 0.5(1) = 3

PTS: 2 REF: 011916aii NAT: F.BF.A.2 TOP: Sequences 110 ANS: 4 PTS: 2 REF: 061921aii NAT: A.APR.B.3

TOP: Graphing Polynomial Functions 111 ANS: 3

x + 1 = x + 1

x + 1 = x 2 + 2x + 1

0 = x2 + x

0 = x(x + 1)

x = −1,0


112 ANS: 3x3 + x2 + 3xy + y = x2 (3x + 1) + y(3x + 1) = x 2 + y

(3x + 1)

PTS: 2 REF: 011828aii NAT: A.SSE.A.2 TOP: Factoring PolynomialsKEY: factoring by grouping

113 ANS: 184.1% × 750 ≈ 631


114 ANS: 72x − 2

x + 1 = 14

7x + 7− 4x2x 2 + 2x

= 14

2x 2 + 2x = 12x + 28

x 2 − 5x − 14 = 0

(x − 7)(x + 2) = 0

x = 7,−2


ID: A

19

115 ANS: 2x = 4y + 5

x − 5 = 4y

14 x − 5

4 = y


116 ANS: 2

x =y

y + 2

xy + 2x = y

xy − y = −2x

y(x − 1) = −2x

y = −2xx − 1


117 ANS: 3 PTS: 2 REF: 061906aii NAT: F.LE.A.2TOP: Families of Functions

118 ANS: 250(1) + 2450 = 2700 The maximum lung capacity of a person is 2700 mL.

PTS: 2 REF: 081928aii NAT: F.IF.B.4 TOP: Graphing Trigonometric Functions 119 ANS:

John found the means of the scores of the two rooms and subtracted the means. The mean score for the classical room was 7 higher than the rap room (82-75). Yes, there is less than a 5% chance this difference occurring due to random chance. It is likely the difference was due to the music.

PTS: 4 REF: 081836aii NAT: S.IC.B.5 TOP: Analysis of Data 120 ANS:

x 2 y53

x 3 y44=

x23 y

53

x34 y

=x

812 y

2012

x912 y

1212

= x−

112 y

23


121 ANS: 2 PTS: 2 REF: 081904aii NAT: A.SSE.A.2TOP: Factoring Polynomials KEY: higher power

ID: A

20

122 ANS:

y = 14(2) (x − 4)2 − 3 y = −1+ −5

2 = −3. The vertex is (4,−3) and p = 2.

PTS: 4 REF: 061935aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions 123 ANS:

h(2) − h(1)2 − 1 = −12, h(t) = 0 at t ≈ 2.2,3.8, using a graphing calculator to find where h(t) = 0.

PTS: 4 REF: 061836aii NAT: F.IF.B.4 TOP: Graphing Trigonometric Functions 124 ANS: 4

f(x) = (x + 1)(x − 1)(x − 2) = (x2 − 1)(x − 2) = x3 − 2x2 − x + 2

PTS: 2 REF: 081921aii NAT: A.APR.B.3 TOP: Graphing Polynomial Functions 125 ANS:

P(−2) = 60 Q(−2) = 0 (x + 2) is a factor of Q(x) since Q(−2) = 0.

PTS: 2 REF: 081929aii NAT: A.APR.B.2 TOP: Remainder Theorem 126 ANS:

P(x) = R(x) −C(x) = −330x 3 + 9000x2 − 67000x + 167000 Least profitable at year 5 because there is a minimum in P(x). Most profitable at year 13 because there is a maximum in P(x).

PTS: 6 REF: 081837aii NAT: F.IF.C.7 TOP: Graphing Polynomial Functions 127 ANS: 4

1313 + 11 = 13

24

PTS: 2 REF: 012011aii NAT: S.CP.A.4 TOP: Conditional Probability

ID: A

21

128 ANS: 2(0.042) = 0.084 ≈ 0.08 The percent of users making in-app purchases will be within 8% of 35%.


x + 2 x4 + 2x 3 + 4x − 10x3 + 4

x4 + 2x3

4x − 10

4x + 8

− 18

x3 + 4 − 18x + 2 . No, because there is a remainder.


130 ANS: 4 PTS: 2 REF: 061907aii NAT: A.APR.B.2TOP: Remainder Theorem

131 ANS: 285

210+ 85

PTS: 2 REF: 081818aii NAT: S.CP.A.1 TOP: Venn Diagrams 132 ANS:

20e .05t = 30e .03t

23 e .05t

e .05t = e .03t

e .05t

ln 23 = lne−.02t

ln 23 = −.02t lne

ln 23

−.02 = t

20.3 ≈ t

PTS: 2 REF: 011829aii NAT: A.REI.D.11 TOP: Other Systems 133 ANS: 3 PTS: 2 REF: 012002aii NAT: F.BF.A.1

TOP: Operations with Functions

ID: A

22

134 ANS: p(8) − p(4)

8 − 4 ≈ 48.78

PTS: 2 REF: 081827aii NAT: F.IF.B.6 TOP: Rate of Change 135 ANS: 4

3x − (−2x + 14) = 16

5x = 30

x = 6

3(6) − 4z = 2

−4z = −16

z = 4

PTS: 2 REF: 011803aii NAT: A.REI.C.6 TOP: Solving Linear SystemsKEY: three variables

136 ANS: 13.9 − 9.4

4 − 1 = 1.5 The average rate of change in the number of hours of daylight from January 1-April 1 is 1.5.


23x + 1 = 1

x − 6x3x + 1

6x + 23x + 1 = 1

x

6x2 + 2x = 3x + 1

6x2 − x − 1 = 0

(2x − 1)(3x + 1) = 0

x = 12 ,−1

3

−13 is extraneous.


a + 4b + 6c = 23

a + 2b + c = 2

2b + 5c = 21

a + 2b + c = 2

−a + 6b + 2c = 14

8b + 3c = 16

8b + 3c = 16

8b + 20c = 84

17c = 68

c = 4

2b + 5(4) = 21

2b = 1

b = 12

a + 4 12

+ 6(4) = 23

a + 2+ 24 = 23

a = −3


139 ANS: 4 PTS: 2 REF: 011805aii NAT: F.LE.B.5TOP: Modeling Exponential Functions

ID: A

23

140 ANS: −1

22 + (−1)2= − 1

5

PTS: 2 REF: 061832aii NAT: F.TF.A.2 TOP: Determining Trigonometric FunctionsKEY: extension to reals

141 ANS: 1

−4(−1) − 3 = 1 8 = 2πb

b = π4

PTS: 2 REF: 081820aii NAT: F.IF.B.4 TOP: Graphing Trigonometric FunctionsKEY: maximum/minimum

142 ANS: 2 PTS: 2 REF: 081908aii NAT: F.IF.B.4TOP: Graphing Polynomial Functions

143 ANS: 2

S 20 =.01 −.01(3)20

1− 3 = 17,433,922


5000 1 + .03512

12 ⋅ 6

≈ 6166.50

PTS: 2 REF: 081917aii NAT: A.CED.A.1 TOP: Exponential Growth 145 ANS: 4 PTS: 2 REF: 081817aii NAT: F.BF.B.3

TOP: Transformations with Functions 146 ANS:

103110+ 103 = 103

213

PTS: 2 REF: 061825aii NAT: S.CP.A.4 TOP: Conditional Probability 147 ANS: 3 PTS: 2 REF: 061910aii NAT: F.BF.A.2

TOP: Sequences 148 ANS: 3

c2 − d 2

d 2 + cd − 2c2 =(c + d)(c − d)(d + 2c)(d − c) =

−(c + d)d + 2c = −c − d

d + 2c


ID: A

24

149 ANS: 18 + 1

6 = 1tb

; 24tb

8 +24tb

6 =24tb

tb

3tb + 4tb = 24

tb =247 ≈ 3.4

PTS: 2 REF: 011827aii NAT: A.CED.A.1 TOP: Modeling Rationals 150 ANS: 2

x2 = 3x + 40

x2 − 3x − 40 = 0

(x − 8)(x + 5) = 0

x = 8,−5

. x = −5 is an extraneous solution.


151 ANS: 2P(B) ⋅P(A| B) = P(A and B)

P(B) ⋅0.8 = 0.2

P(B) = 0.25

PTS: 2 REF: 081913aii NAT: S.CP.A.3 TOP: Conditional Probability 152 ANS: 1

x − 4x − 1 = 2

x(x − 1) − 4 = 2(x − 1)

x2 − x − 4 = 2x − 2

x2 − 3x − 2 = 0

x =3 ± (−3)2 − 4(1)(−2)

2(1) =3 ± 17

2


153 ANS: 2

x =2 ± (−2)2 − 4(5)(4)

2(5) =2 ± −76

10 =2 ± i 4 19

10 = 15 ±

i 195


ID: A

25

154 ANS: 4

PTS: 2 REF: 011924aii NAT: A.REI.D.11 TOP: Other Systems 155 ANS: 4

120 = 68 + (195 − 68)e−0.05t

52 = 127e−0.05t

ln 52127 = lne−0.05t

ln 52127 = −0.05t

ln 52127

−0.05 = t

18 ≈ t

PTS: 2 REF: 081918aii NAT: F.LE.A.4 TOP: Exponential Decay 156 ANS: 4

The vertex is (2,2) and p = 3. 3 + 2 = 5

PTS: 2 REF: 081823aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions 157 ANS:

x2 + (x − 28)2 = 400

x2 + x2 − 56x + 784 = 400

2x 2 − 56x + 384 = 0

x2 − 28x + 192 = 0

(x − 16)(x − 12) = 0

x = 12,16

y = 12− 28 = −16 y = 16− 28 = −12


29.101 ± 2 ⋅0.934 = 27.23− 30.97. Yes, since 30 falls within the 95% interval.

PTS: 4 REF: 011935aii NAT: S.IC.A.2 TOP: Analysis of Data

ID: A

26

159 ANS: 2 PTS: 2 REF: 081802aii NAT: S.IC.B.3TOP: Analysis of Data KEY: type

160 ANS:

No. x27

x 35

= x27 ⋅ x

35 = x

3135 = x3135



162 ANS: 1

x − 20x = 8

x 2 − 8x − 20 = 0

(x − 10)(x + 2) = 0

x = 10,−2

PTS: 2 REF: 061916aii NAT: A.CED.A.1 TOP: Modeling Rationals 163 ANS: 3

ebt = ca

lnebt = ln ca

bt lne = ln ca

t =ln c

ab

PTS: 2 REF: 011813aii NAT: F.LE.A.4 TOP: Exponential Growth 164 ANS: 4

(a + b + c)2 = a 2 + ab + ac + ab + b 2 + bc + ac + ab + c2

x = a 2 + b 2 + c2 + 2(ab + bc + ac)

x = y + 2z

PTS: 2 REF: 061822aii NAT: A.APR.C.4 TOP: Polynomial Identities

ID: A

27

165 ANS: 2x2 + 4x − 1 = x − 3

x 2 + 3x + 2 = 0

(x + 2)(x + 1) = 0

x = −2,−1

y + 3 = −1

y = −4


C(t) = 63000 1+ 0.025512

12t

63000 1+ 0.025512

12t

= 100000

12t log(1.002125) = log 10063

t ≈ 18.14

PTS: 4 REF: 061835aii NAT: A.CED.A.1 TOP: Exponential Growth 167 ANS:


x + 6 2x 4 + 8x3 − 25x 2 − 6x + 14

2x4 + 12x3

− 4x3 − 25x 2

− 4x3 − 24x 2

− x2 − 6x

− x 2 − 6x

2x3 − 4x2 − x + 14x + 6


ID: A

28

169 ANS:

period = 2π0.8π = 2.5. The wheel rotates once every 2.5 seconds. No, because the maximum

of f(t) = 26.


170 ANS: 2 PTS: 2 REF: 061804aii NAT: S.ID.B.6TOP: Regression KEY: choose model

171 ANS:

antibiotic n(0) = 0+ 10+ 5 + 18

02 + 8(0) + 15= 3

15 + 1815 = 21

15

a(0) = 90+ 3 = 3

t + 1t + 5 + 18

t2 + 8t + 15= 9

t + 3

(t + 1)(t + 3)(t + 5)(t + 3) +

18(t + 3)(t + 5) =

9(t + 5)(t + 3)(t + 5)

t2 + 4t + 3+ 18 = 9t + 45

t2 − 5t − 24 = 0

(t − 8)(t + 3) = 0

t = 8


172 ANS: 4

lne 0.3x = ln 591887

x =ln 5918

870.3

PTS: 2 REF: 081801aii NAT: F.LE.A.4 TOP: Exponential EquationsKEY: without common base

ID: A

29

173 ANS: 2



(1) 0.4 ⋅ 0.3 ≠ 0.2, (2) 0.8 ⋅ 0.25 = 0.2, (3) P(A| B) = P(A) = 0.2

0.2 ≠ 0.2 ⋅0.2

, (4) 0.2 ≠ 0.15 ⋅ 0.05

PTS: 2 REF: 011912aii NAT: S.CP.A.3 TOP: Conditional Probability 176 ANS: 3 PTS: 2 REF: 061824aii NAT: A.CED.A.1

TOP: Modeling Rationals 177 ANS:

x2 − 6x = −17

x2 − 6x + 9 = −17+ 9

(x − 3)2 = −8

x − 3 = ±2i 2

x = 3± 2i 2

The solution is imaginary because the parabola and line do not intersect.

PTS: 4 REF: 081936aii NAT: A.REI.B.4 TOP: Solving QuadraticsKEY: complex solutions | completing the square

178 ANS: 17 − 3i + x2 − 4xi + 4i2 − 4i − 2x2 = 7 − 7i − x2 − 4xi − 4 = 3 − x2 − 4xi − 7i = (3 − x2 ) − (4x + 7)i


ID: A

30

179 ANS:

y = 2sin4x


180 ANS: Self selection is a cause of bias because people with more free time are more likely to respond.

PTS: 2 REF: 061828aii NAT: S.IC.B.3 TOP: Analysis of DataKEY: bias

181 ANS: 3 x − 2x = −5

3 x = 2x − 5

9x = 4x 2 − 20x + 25

4x 2 − 29x + 25 = 0

(4x − 25)(x − 1) = 0

x = 254 ,1

1 is extraneous.


182 ANS: 12) linear, 3) quadratic, 4) cubic

PTS: 2 REF: 061920aii NAT: F.LE.A.2 TOP: Families of Functions 183 ANS: 3 PTS: 2 REF: 081909aii NAT: F.BF.A.2

TOP: Sequences KEY: recursive 184 ANS:

PTS: 2 REF: 011926aii NAT: F.IF.C.7 TOP: Graphing Polynomial Functions

ID: A

31

185 ANS: 4 PTS: 2 REF: 081912aii NAT: F.IF.C.7TOP: Graphing Trigonometric Functions KEY: mixed

186 ANS: 4 PTS: 2 REF: 011808aii NAT: A.SSE.B.3TOP: Modeling Exponential Functions

187 ANS: 4wx 2 +w = 0

w(x2 + 1) = 0

x2 = −1

x = ±i

PTS: 2 REF: 061912aii NAT: A.REI.B.4 TOP: Solving QuadraticsKEY: complex solutions | taking square roots


189 ANS:

P(F| L) = 1227 P(F) = 22

45 Since P(F| L) ≠ P(F), the events are not independent.



191 ANS: 2

PTS: 2 REF: 061817aii NAT: S.ID.A.4 TOP: Normal DistributionsKEY: probability

ID: A

32

192 ANS: 138.905± 2 ⋅ 7.95 = 123− 155. No, since 125 (50% of 250) falls within the 95% interval.

PTS: 4 REF: 011835aii NAT: S.IC.A.2 TOP: Analysis of Data 193 ANS: 1

x2 + 2x + 1 = (x + 1)2

PTS: 2 REF: 011919aii NAT: A.APR.B.3 TOP: Graphing Polynomial Functions 194 ANS: 1

2000 1 + .03212

12t

≈ 2000(1.003)12t

PTS: 2 REF: 012004aii NAT: F.BF.A.1 TOP: Modeling Exponential Functions 195 ANS: 1

3x + 1 9x2 + 0x − 23x − 1

9x2 + 3x

− 3x − 2

−3x − 1

− 1


196 ANS: 1

PTS: 2 REF: 011908aii NAT: F.IF.B.4 TOP: Graphing Polynomial Functions 197 ANS: 2 PTS: 2 REF: 061816aii NAT: F.IF.C.7

TOP: Graphing Polynomial Functions KEY: bimodalgraph

ID: A

33

198 ANS: 1

100 12

d8= 100ekd

12

18= ek

k ≈ −0.087


a 1 = 4

an = 3an − 1


200 ANS: 1

PTS: 2 REF: 081919aii NAT: S.ID.A.4 TOP: Normal DistributionsKEY: percent

ID: A

34

201 ANS: B = 1.69 30 + 4.45 − 3.49 ≈ 6, which is a steady breeze. 15 = 1.69 s + 4.45 − 3.49

18.49 = 1.69 s + 4.45

18.491.69 = s + 4.45

18.491.69

2

= s + 4.45

s = 18.491.69

2

− 4.45

s ≈ 115

9.5 = 1.69 s + 4.45 − 3.49

12.99 = 1.69 s + 4.45

12.991.69 = s + 4.45

12.991.69

2

= s + 4.45

s = 12.991.69

2

− 4.45

s ≈ 55

10.49 = 1.69 s + 4.45 − 3.49

13.98 = 1.69 s + 4.45

13.981.69 = s + 4.45

13.981.69

2

= s + 4.45

s = 13.981.69

2

− 4.45

s ≈ 64

55-64

PTS: 6 REF: 081937aii NAT: A.REI.A.2 TOP: Solving RadicalsKEY: context

202 ANS: 19110 = 5000e30r

ln 911500 = lne30r

ln 91150030 = r

r ≈.02


S 7 =85000 − 85000(1.06)7

1 − 1.06 ≈ 713476.20


ID: A

35

204 ANS: 1 PTS: 2 REF: 081804aii NAT: F.IF.C.9TOP: Comparing Functions

205 ANS: 4(1) and (3) are not recursive


206 ANS:

s(t) = 200(0.5)t

15 110 = (0.5)

t15

log 110 = log(0.5)

t15

−1 =t ⋅ log(0.5)

15

t = −15log(0.5) ≈ 50


(x + 4)2 − 10 = 3x + 6

x 2 + 8x + 16 − 10 = 3x + 6

x2 + 5x = 0

x(x + 5) = 0

x = −5,0

y = 3(−5) + 6 = −9

y = 3(0) + 6 = 6


PTS: 2 REF: 081932aii NAT: A.REI.D.11 TOP: Other Systems 209 ANS: 2 PTS: 2 REF: 081816aii NAT: F.IF.C.7

TOP: Graphing Logarithmic Functions KEY: bimodalgraph

ID: A

36

210 ANS: 4x + 6y − 8z = −2

4x − 8y + 20z = 12

−4x + y + z = 16

4x + 6y − 8z = −2

−4x + y + z = 16

7y − 7z = 14

y − z = 2

y = z + 2

4x − 8y + 20z = 12

−4x + y + z = 16

−7y + 21z = 28

y − 3z = −4

y = 3z − 4

z + 2 = 3z − 4

6 = 2z

z = 3

y = 3+ 2

= 5

−4x + 5 + 3 = 16

−4x = 8

x = −2


211 ANS: 2

5x 2 − 4x + 2 = 0 4± (−4)2 − 4(5)(2)

2(5) =4 ± −24

10 =4 ± 2i 6

10 =2 ± i 6

5


212 ANS: 1N(6) −N(0)

6 − 0 ≈ −8.93


x + y − z = 6

−x + 4y − z = 17

5y − 2z = 23

2x + 2y − 2z = 12

2x − 3y + 2z = −19

5y − 4z = 31

5y − 4z = 31

5y − 2z = 23

−2z = 8

z = −4

5y − 2(−4) = 23

5y = 15

y = 3

x + 3 − (−4) = 6

x = −1


214 ANS: 10.1 − −2

2 − 2.5 − −0.12 = 6.05 − 1.3 = 4.75

PTS: 2 REF: 081930aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: amplitude

ID: A

37

215 ANS: (a + b)3 = a 3 + b 3

a 3 + 3a 2 b + 3ab 2 + b 3 = a 3 + b 3

3ab 2 + 3a 2b = 0

3ab(b + a) = 0

a = 0,b = 0,a = −b

No. Erin’s shortcut only works if a = 0, b = 0 or a = −b.


(x 6y4 − 9)(x4 − 16)

(x3 y2 + 3)(x3 y2 − 3)(x2 + 4)(x2 − 4)


217 ANS: 4

x(x − 2) 10x 2 − 2x

+ 4x = 5

x − 2

10 + 4(x − 2) = 5x

10 + 4x − 8 = 5x

2 = x

2 is extraneous.


218 ANS: P(A +B) = P(A) ⋅P(B| A) = 0.8 ⋅0.85 = 0.68



In vertex form, the parabola is y = − 14(2) (x + 4)2 + 3. The vertex is (−4,3) and p = 2. 3 + 2 = 5

PTS: 2 REF: 011816aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions

ID: A

38

221 ANS: 1 PTS: 2 REF: 081903aii NAT: F.LE.A.2TOP: Families of Functions

222 ANS: 3T(19) = 8sin(0.3(19) − 3) + 74 ≈ 77

PTS: 2 REF: 061922aii NAT: F.TF.A.2 TOP: Determining Trigonometric FunctionsKEY: radians

223 ANS: 2n 2 n 2 − 9

+ 4n n 2 − 9

− 12 n 2 − 9

n 2 + 4n − 12

n 2 − 9

(n + 6)(n − 2)(n + 3)(n − 3)


224 ANS: No. 0.499 ± 2(0.049) → 0.401− 0.597. Since 0.43 falls within this interval, Robin’s coin is likely not unfair.


a = 14− 42 = 5, d = 14+ 4

2 = 9

PTS: 2 REF: 061810aii NAT: F.TF.B.5 TOP: Modeling Trigonometric Functions 226 ANS: 1

(x32 )2 = x3


227 ANS: q has the smaller minimum value for the domain [−2,2]. h’s minimum is −1 2(−1) + 1

and q’s minimum is −8.

PTS: 2 REF: 011830aii NAT: F.IF.C.9 TOP: Comparing Functions 228 ANS:

N(t) = 950e0.0475t The base is e because growth is continuous. N 3624

≈ 1020

PTS: 4 REF: 081933aii NAT: F.LE.A.2 TOP: Modeling Exponential Functions 229 ANS: 4 PTS: 2 REF: 011801aii NAT: S.IC.B.3

TOP: Analysis of Data KEY: bias

ID: A

39

230 ANS: x2 − 6

x 2 + 2

PTS: 2 REF: 081825aii NAT: A.SSE.A.2 TOP: Factoring PolynomialsKEY: higher power

231 ANS: 40.48 ⋅ 0.25 = 0.12

PTS: 1 REF: 061811aii NAT: S.CP.A.2 TOP: Probability of Compound EventsKEY: probability

232 ANS: 4

1 + .00912 = 1.00075


A(t) = 318000(1.07) t 318000(1.07) t = 1000000

1.07t = 1000318

t log1.07 = log 1000318

t =log 1000

318log1.07

t ≈ 17

The graph of A(t) nearly intersects

the point (17,1000000).

PTS: 6 REF: 011937aii NAT: A.CED.A.1 TOP: Exponential Growth 234 ANS: 3

The vertex is (−3,5) and p = 2. y = −14(2) (x + 3)2 + 5

PTS: 2 REF: 011914aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions 235 ANS: 3 PTS: 2 REF: 011824aii NAT: F.BF.A.2

TOP: Sequences

ID: A

40

236 ANS: 2u = x + 2 u 2 + 4u + 3

(u + 3)(u + 1)

(x + 2+ 3)(x + 2+ 1)

(x + 5)(x + 3)


237 ANS: 165+ 66− 33

825 = 198825

PTS: 2 REF: 081925aii NAT: S.CP.B.6 TOP: Conditional Probability 238 ANS: 1

x3 + 2x2 − 9x − 18 = 0

x 2 (x + 2) − 9(x + 2) = 0

x3 − 9x + 2x 2 − 18 = 0

x(x2 − 9) + 2(x 2 − 9) = 0

x3 − 9x + 2x2 − 18 = 0

x(x 2 − 9) + 2(x 2 − 9) = 0

(x + 2)(x 2 − 9) = 0

PTS: 2 REF: 011903aii NAT: A.APR.B.3 TOP: Solving Polynomial Equations

ID: A

1

Algebra II Regents at RandomAnswer Section

239 ANS: 3

d = 10log 6.3× 10−3

1.0 × 10−12 ≈ 98

PTS: 2 REF: 011715aii NAT: F.IF.B.4 TOP: Evaluating Logarithmic Expressions 240 ANS:

0 = x2 (x + 1) − 4(x + 1)

0 = (x2 − 4)(x + 1)

0 = (x + 2)(x − 2)(x + 1)

x = −2,−1,2


56− x = x

56 − x = x2

0 = x2 + x − 56

0 = (x + 8)(x − 7)

x = 7

−8 is extraneous.


242 ANS: 2The 2010 population is 110 million.

PTS: 2 REF: 061718aii NAT: F.LE.B.5 TOP: Modeling Exponential Functions 243 ANS:

sample: pails of oranges; population: truckload of oranges. It is likely that about 5% of all the oranges are unsatisfactory.

PTS: 2 REF: 011726aii NAT: S.IC.A.2 TOP: Analysis of Data

ID: A

2

244 ANS: 4m(c)g(c) = c + 1

1 − c 2 = c + 1(1+ c)(1 − c) =

11− c

PTS: 2 REF: 061608aii NAT: F.BF.A.1 TOP: Operations with Functions 245 ANS: 1 PTS: 2 REF: 061708aii NAT: F.TF.B.5

TOP: Modeling Trigonometric Functions 246 ANS: 1

The graph of y = sinx is unchanged when rotated 180º about the origin.

PTS: 2 REF: 081614aii NAT: F.BF.B.3 TOP: Even and Odd Functions 247 ANS:

r = 360300 = 1.2 Sn =

300 − 300(1.2)n

1 − 1.2 S 10 =300 − 300(1.2)10

1− 1.2 ≈ 7787.6

PTS: 2 REF: 012029aii NAT: A.SSE.B.4 TOP: Series 248 ANS:

Sn =33000 − 33000(1.04)n

1 − 1.04 S 15 =33000− 33000(1.04)15

1 − 1.04 ≈ 660778.39


2(x − 4)(x + 3)(x − 4) +

3(x + 3)(x − 4)(x + 3) =

2x − 2x2 − x − 12

2x − 8+ 3x + 9 = 2x − 2

3x = −3

x = −1


250 ANS: 2

x + 2σ represents approximately 48% of the data.


251 ANS: 3 PTS: 2 REF: 061720aii NAT: F.LE.A.2TOP: Sequences KEY: explicit

ID: A

3

252 ANS:

p 2n12

8

p 5 n 4 = p 16 n 4

p 2n 2 p = p 18 n 6 p

PTS: 2 REF: 012025aii NAT: N.RN.A.2 TOP: Radicals and Rational Exponents 253 ANS:

20000 = PMT1 − (1+.00625)−60

0.00625

PMT ≈ 400.76

21000− x = 3001− (1 +.00625)−60

0.00625

x ≈ 6028


f(4) = 2(4)3 − 5(4)2 − 11(4) − 4 = 128 − 80 − 44 − 4 = 0 Any method that demonstrates 4 is a zero of f(x) confirms

that x − 4 is a factor, as suggested by the Remainder Theorem.

PTS: 2 REF: spr1507aii NAT: A.APR.B.2 TOP: Remainder Theorem

ID: A

4

255 ANS:

A(t) = 800e−0.347t

B(t) = 400e−0.231t

800e−0.347t = 400e−0.231t

ln2e−0.347t = lne−0.231t

ln2 + lne−0.347t = lne−0.231t

ln2 − 0.347t = −0.231t

ln2 = 0.116t

6 ≈ t

0.15 = e−0.347t

ln0.15 = lne−0.347t

ln0.15 = −0.347t ⋅ lne

5.5 ≈ t


306.25− 156.2570− 50 = 150

20 = 7.5 Between 50-70 mph, each additional mph in speed requires 7.5 more feet to stop.


P(P / K) =P(P^K)

P(K) = 1.92.3 ≈ 82.6% A key club member has an 82.6% probability of being enrolled in AP Physics.

PTS: 4 REF: 011735aii NAT: S.CP.B.6 TOP: Conditional Probability

ID: A

5

258 ANS:

7 = 20(0.5)t

8.02

log0.35 = log0.5t

8.02

log0.35 =t log0.5

8.02

8.02log0.35log0.5 = t

t ≈ 12

PTS: 4 REF: 081634aii NAT: F.LE.A.4 TOP: Exponential Decay 259 ANS:

100 = 140 12

5h

log 100140 = log 1

2

5h

log 57 = 5

h log 12

h =5log 1

2

log 57

≈ 10.3002

40 = 140 12

t10.3002

log 27 = log 1

2

t10.3002

log 27 =

t log 12

10.3002

t =10.3002log 2

7

log 12

≈ 18.6


(2 − yi)(2 − yi) = 4− 4yi + y2 i2 = −y2 − 4yi + 4


y = 5−t = 15

t

PTS: 2 REF: 061615aii NAT: F.IF.C.7 TOP: Graphing Exponential Functions

ID: A

6

262 ANS: 3Self selection causes bias.


263 ANS:

M = 172600 •0.00305(1+ 0.00305)12 ⋅ 15

(1 + 0.00305)12 ⋅ 15 − 1≈ 1247 1100 = (172600− x) •

0.00305(1 + 0.00305)12 ⋅ 15

(1+ 0.00305)12 ⋅ 15 − 1

1100 ≈ (172600− x) • (0.007228)

152193 ≈ 172600 − x

20407 ≈ x


The vertex of the parabola is (4,−3). The x-coordinate of the focus and the vertex is the same. Since the distance from the vertex to the directrix is 3, the distance from the vertex to the focus is 3, so the y-coordinate of the focus is 0. The coordinates of the focus are (4,0).

PTS: 2 REF: 061630aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions 265 ANS: 2

2x + 3 4x3 + 0x2 + 5x + 102x2 − 3x + 7

4x3 + 6x 2

− 6x 2 + 5x

−6x 2 − 9x

14x + 10

14x + 21

− 11


ID: A

7

266 ANS: Randomly assign participants to two groups. One group uses the toothpaste with ingredient X and the other group uses the toothpaste without ingredient X.

PTS: 2 REF: 061626aii NAT: S.IC.B.3 TOP: Analysis of DataKEY: type

267 ANS:

vertex (3,6), focus (3,1), p = 5, directrix y = 6 + 5 = 11


The maximum volume of p(x) = −(x + 2)(x − 10)(x − 14) is about 56, at x = 12.1

PTS: 2 REF: 081712aii NAT: F.IF.B.4 TOP: Graphing Polynomial Functions 269 ANS: 1

The zeros of the polynomial are at −b, and c. The sketch of a polynomial of degree 3 with a negative leading coefficient should have end behavior showing as x goes to negative infinity, f(x) goes to positive infinity. The multiplicities of the roots are correctly represented in the graph.

PTS: 2 REF: spr1501aii NAT: F.IF.C.7 TOP: Graphing Polynomial FunctionsKEY: bimodalgraph

270 ANS: 2

x + 2 x3 + 2x2 + x + 6x2 + 0x + 1

x 3 + 2x2

0x2 + x

0x 2 + 0x

x + 6

x + 2

4


ID: A

8

271 ANS: 2 PTS: 2 REF: 061620aii NAT: F.IF.B.4TOP: Graphing Polynomial Functions

272 ANS: 3f(x) = −f(x), so f(x) is odd. g(−x) ≠ g(x), so g(x) is not even. g(−x) ≠ −g(x), so g(x) is not odd. h(−x) = h(x), so h(x) is even.

PTS: 2 REF: fall1502aii NAT: F.BF.B.3 TOP: Even and Odd Functions 273 ANS: 2

x =y + 1y − 2

xy − 2x = y + 1

xy − y = 2x + 1

y(x − 1) = 2x + 1

y = 2x + 1x − 1


274 ANS: 0.602 ± 2 ⋅ 0.066 = 0.47− 0.73. Since 0.50 falls within the 95% interval, this supports the concern there may be an even split.


sin2θ + (−0.7)2 = 1

sin2θ =.51

sinθ = ± .51

Since θ is in Quadrant II, sinθ = .51 and tanθ = sinθcosθ =

.51−0.7 ≈ −1.02

PTS: 2 REF: 081628aii NAT: F.TF.C.8 TOP: Determining Trigonometric Functions

ID: A

9

276 ANS:

x − 5 = −x + 7

x − 5 = x 2 − 14x + 49

0 = x2 − 15x + 54

0 = (x − 6)(x − 9)

x = 6, 9

x − 5 = −9 + 7 = −2 is extraneous.

PTS: 2 REF: spr1508aii NAT: A.REI.A.2 TOP: Solving RadicalsKEY: extraneous solutions

277 ANS: The mean difference between the students’ final grades in group 1 and group 2 is –3.64. This value indicates that students who met with a tutor had a mean final grade of 3.64 points less than students who used an on-line subscription. One can infer whether this difference is due to the differences in intervention or due to which students were assigned to each group by using a simulation to rerandomize the students’ final grades many (500) times. If the observed difference –3.64 is the result of the assignment of students to groups alone, then a difference of –3.64 or less should be observed fairly regularly in the simulation output. However, a difference of –3 or less occurs in only about 2% of the rerandomizations. Therefore, it is quite unlikely that the assignment to groups alone accounts for the difference; rather, it is likely that the difference between the interventions themselves accounts for the difference between the two groups’ mean final grades.

PTS: 4 REF: fall1514aii NAT: S.IC.B.5 TOP: Analysis of Data 278 ANS: 4

period = 2πB

160 = 2π

B

B = 120π

PTS: 2 REF: 061624aii NAT: F.TF.B.5 TOP: Modeling Trigonometric Functions 279 ANS: 3

1.0525112 ≈ 1.00427

PTS: 2 REF: 061621aii NAT: F.BF.A.1 TOP: Modeling Exponential Functions 280 ANS: 4 PTS: 2 REF: 081624aii NAT: F.BF.A.2

TOP: Sequences

ID: A

10

281 ANS: 4 PTS: 2 REF: 081718aii NAT: F.IF.C.7TOP: Graphing Trigonometric Functions KEY: amplitude

282 ANS: r(2) = −6. Since there is a remainder when the cubic is divided by x − 2, this binomial is not a factor.

2 1 -4 4 62 -4 0

1 -2 0 -6


4(x2 − 6x + 9) + 4(y2 + 18y + 81) = 76+ 36+ 324

4(x − 3)2 + 4(y + 9)2 = 436

PTS: 2 REF: 061619aii NAT: G.GPE.A.1 TOP: Equations of CirclesKEY: completing the square

284 ANS: 1x2 + 2x − 8 = 0

(x + 4)(x − 2) = 0

x = −4,2

PTS: 2 REF: 081701aii NAT: A.APR.D.6 TOP: Undefined Rationals 285 ANS: 4

−54x9

y4

23

=(2 ⋅ −27)

23 x

183

y83

= 223 ⋅ 9x6

y2 ⋅ y23

=9x6 43

y2 y23


ID: A

11

286 ANS:

y = −x + 5

(x − 3)2 + (−x + 5 + 2)2 = 16

x 2 − 6x + 9 + x2 − 14x + 49 = 16

2x2 − 20x + 42 = 0

x2 − 10x + 21 = 0

(x − 7)(x − 3) = 0

x = 7,3

y = −7 + 5 = −2

y = −3 + 5 = 2


0.506 ± 2 ⋅ 0.078 = 0.35− 0.66. The 32.5% value falls below the 95% confidence level.


1J = 1

F − 1W

1J = W −F

FW

J = FWW − F


289 ANS: Using a 95% level of confidence, x ± 2 standard deviations sets the usual wait time as 150-302 seconds. 360 seconds is unusual.

PTS: 2 REF: 081629aii NAT: S.IC.B.6 TOP: Analysis of Data

ID: A

12

290 ANS:

720 =120000 .048

12

1 + .04812

n

1+ .04812

n

− 1

720(1.004)n − 720 = 480(1.004)n

240(1.004)n = 720

1.004n = 3

n log1.004 = log3

n ≈ 275.2 months

275.212 ≈ 23 years

PTS: 4 REF: spr1509aii NAT: A.CED.A.1 TOP: Exponential Growth 291 ANS: 1

A reference triangle can be sketched using the coordinates (−4,3) in the second quadrant to find the value of sinθ .

PTS: 2 REF: spr1503aii NAT: F.TF.A.2 TOP: Determining Trigonometric FunctionsKEY: extension to reals

292 ANS:

PTS: 2 REF: fall1510aii NAT: A.REI.D.11 TOP: Other Systems

ID: A

13

293 ANS: The expression is of the form y 2 − 5y − 6 or (y − 6)(y + 1). Let y = 4x 2 + 5x :

4x2 + 5x − 6

4x 2 + 5x + 1

(4x − 3)(x + 2)(4x + 1)(x + 1)

PTS: 2 REF: fall1512aii NAT: A.SSE.A.2 TOP: Factoring PolynomialsKEY: a>1

294 ANS: 1

x =−3 ± 32 − 4(2)(2)

2(2) =−3± −7

4 = −34 ±

i 74


295 ANS: 4 PTS: 2 REF: 061706aii NAT: F.IF.B.4TOP: Graphing Trigonometric Functions

296 ANS: 4 PTS: 2 REF: 061601aii NAT: N.RN.A.2TOP: Radicals and Rational Exponents KEY: variables

297 ANS: 2



(2) is not recursive


ID: A

14

300 ANS: 1x − 1

3 = − 13x

3− x3x = − 1

3x

3 − x = −1

x = 4


301 ANS: 4

The vertex is (2,−1) and p = 2. y = − 14(2) (x − 2)2 − 1

PTS: 2 REF: 081619aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions 302 ANS: 3 PTS: 2 REF: 011708aii NAT: F.BF.B.4

TOP: Inverse of Functions KEY: other 303 ANS: 1


−2 −12 x2 = −6x + 20

x2 − 12x = −40

x 2 − 12x + 36 = −40 + 36

(x − 6)2 = −4

x − 6 = ±2i

x = 6± 2i

PTS: 2 REF: fall1504aii NAT: A.REI.B.4 TOP: Solving QuadraticsKEY: complex solutions | completing the square

ID: A

15

305 ANS: x + y + z = 1

x + 2y + 3z = 1

−x + 3y − 5z = 11

x + y + z = 1

x + 2y + 3z = 1

y + 2z = 0

y = −2z

x + y + z = 1

−x + 3y − 5z = 11

4y − 4z = 12

y − z = 3

−2z − z = 3

−3z = 3

z = −1

y − (−1) = 3

y = 2

x + 2 − 1 = 1

x = 0


306 ANS: 1II. Ninth graders drive to school less often; III.Students know little about adults; IV. Calculus students love math!


307 ANS: 12x

x − 2xx

−11x

x − 2x − 2

=8

x2 − 2x

2x 2 − 11x + 22 = 8

2x 2 − 11x + 14 = 0

(2x − 7)(x − 2) = 0

x = 72 ,2



309 ANS: an = xn − 1 (x + 1) xn − 1 = 0

x = 0

x + 1 = 0

x = −1

PTS: 4 REF: spr1511aii NAT: F.LE.A.2 TOP: SequencesKEY: recursive

ID: A

16

310 ANS: 6x − 3y + 2z = −10

−2x + 3y + 8z = 72

4x + 10z = 62

x + 3y + 5z = 45

6x − 3y + 2z = −10

7x + 7z = 35

4x + 4z = 20

4x + 10z = 62

4x + 4z = 20

6z = 42

z = 7

4x + 4(7) = 20

4x = −8

x = −2

6(−2) − 3y + 2(7) = −10

−3y = −12

y = 4

PTS: 4 REF: spr1510aii NAT: A.REI.C.6 TOP: Solving Linear SystemsKEY: three variables

311 ANS: 2

ME = zp(1− p)

n

= 1.96

(0.55)(0.45)900

≈ 0.03 or 1

900≈ 0.03


xi(−6i)2 = xi(36i2 ) = 36xi3 = −36xi


m5 +m3 − 6m = m(m4 +m2 − 6) = m(m2 + 3)(m2 − 2)


314 ANS: 1AP = ert

0.42 = ert

ln0.42 = lne rt

−0.87 ≈ rt

PTS: 2 REF: 011723aii NAT: F.BF.A.1 TOP: Modeling Exponential Functions

ID: A

17

315 ANS:

This scenario can be modeled with a Venn Diagram: Since P(S ∪ I)c = 0.2, P(S ∪ I) = 0.8. Then, P(S ∩ I) = P(S) +P(I) − P(S ∪ I)

= 0.5 + 0.7 − 0.8

= 0.4

If S and I are independent, then the

Product Rule must be satisfied. However, (0.5)(0.7) ≠ 0.4. Therefore, salary and insurance have not been treated independently.

PTS: 4 REF: spr1513aii NAT: S.CP.A.2 TOP: Probability of Compound EventsKEY: independence

316 ANS: 44x2 = −98

x2 = −984

x2 = −492

x = ± −492 = ± 7i

2⋅

22= ±

7i 22

PTS: 2 REF: 061707aii NAT: A.REI.B.4 TOP: Solving QuadraticsKEY: complex solutions | taking square roots

317 ANS: 2 PTS: 2 REF: 081610aii NAT: F.IF.B.4TOP: Graphing Trigonometric Functions KEY: increasing/decreasing

318 ANS: 2

PTS: 2 REF: 081603aii NAT: A.REI.D.11 TOP: Other Systems 319 ANS: 3 PTS: 2 REF: 061722aii NAT: A.CED.A.1


B(t) = 100(2)t

30

PTS: 2 REF: 012031aii NAT: F.LE.A.2 TOP: Modeling Exponential Functions 321 ANS: 4 PTS: 2 REF: 081707aii NAT: F.TF.A.2

TOP: Reference Angles KEY: bimodalgraph

ID: A

18

322 ANS: 4 PTS: 2 REF: 081708aii NAT: A.APR.B.3TOP: Solving Polynomial Equations

323 ANS: Some of the students who did not drink energy drinks read faster than those who did drink energy drinks.

17.7− 19.1 = −1.4 Differences of -1.4 and less occur 25232 or about 10% of the time, so the difference is not

unusual.

PTS: 4 REF: 081636aii NAT: S.IC.B.5 TOP: Analysis of Data 324 ANS: 1 PTS: 2 REF: 081616aii NAT: F.TF.A.1

TOP: Unit Circle KEY: bimodalgraph 325 ANS: 3 PTS: 2 REF: 081618aii NAT: F.LE.A.2

TOP: Sequences KEY: recursive 326 ANS:

100 = 325+ (68 − 325)e−2k

−225 = −257e−2k

k =

ln −225−257

−2

k ≈ 0.066

T = 325− 257e−0.066t

T = 325− 257e−0.066(7) ≈ 163

PTS: 4 REF: fall1513aii NAT: F.LE.A.4 TOP: Exponential Growth 327 ANS:

A t = 100 0.5 t

63 , where t is time in years, and A t is the amount of titanium-44 left after t years. A 10 − A 0

10− 0 = 89.58132 − 10010 = −1.041868 The estimated mass at t = 40 is 100− 40(−1.041868) ≈ 58.3. The

actual mass is A 40 = 100 0.5 4063 ≈ 64.3976. The estimated mass is less than the actual mass.

PTS: 6 REF: fall1517aii NAT: F.LE.A.2 TOP: Modeling Exponential Functions 328 ANS: 3

The pattern suggests an exponential pattern, not linear or sinusoidal. A 4% growth rate is accurate, while a 43% growth rate is not.

PTS: 2 REF: 011713aii NAT: S.ID.B.6 TOP: RegressionKEY: choose model

329 ANS: 3 PTS: 2 REF: 012003aii NAT: A.APR.C.4TOP: Polynomial Identities

ID: A

19

330 ANS:

PTS: 2 REF: 081732aii NAT: F.IF.C.7 TOP: Graphing Polynomial Functions 331 ANS: 1 PTS: 2 REF: 061701aii NAT: A.APR.B.3

TOP: Graphing Polynomial Functions 332 ANS: 2

2121334 ≈.16 ME = z

p(1− p)n

= 1.96

(0.16)(0.84)1334

≈ 0.02 or 1

1334≈.027


The car lost approximately 19% of its value each year.

PTS: 2 REF: 081613aii NAT: F.LE.B.5 TOP: Modeling Exponential Functions 334 ANS:

a 1 = 4

an = 2an − 1 + 1

a 8 = 639


335 ANS: 3

between 000 and 449, inclusive→ 4501000 = 45%

PTS: 2 REF: 012024aii NAT: S.IC.B.3 TOP: Analysis of DataKEY: type

336 ANS: 1

PTS: 2 REF: fall1503aii NAT: A.APR.D.6 TOP: Rational ExpressionsKEY: division

ID: A

20

337 ANS: x3 + 9x3 + 8

= x3 + 8x3 + 8

+ 1x3 + 8

x3 + 9x3 + 8

= x3 + 9x3 + 8


x(x + 7) 3x + 25x + 7 − 5 = 3

x

x(3x + 25) − 5x(x + 7) = 3(x + 7)

3x2 + 25x − 5x2 − 35x = 3x + 21

2x2 + 13x + 21 = 0

(2x + 7)(x + 3) = 0

x = −72 ,−3

PTS: 2 REF: fall1501aii NAT: A.REI.A.2 TOP: Solving RationalsKEY: rational solutions

339 ANS: Light wave C. The periods for A, B, and C are 280, 220 and 320.


340 ANS:

A student is more likely to jog if both siblings jog. 1 jogs: 4162239 ≈ 0.19. both jog: 400

1780 ≈ 0.22


csc θ = 1sinθ , and sinθ on a unit circle represents the y value of a point on the unit circle. Since y = sinθ ,

csc θ = 1y .

PTS: 2 REF: 011727aii NAT: F.TF.A.2 TOP: Reciprocal Trigonometric Relationships 342 ANS:

P(S ∩M) = P(S) + P(M) − P(S ∪M) = 6491376 + 433

1376 − 9741376 = 108

1376

PTS: 2 REF: 061629aii NAT: S.CP.B.7 TOP: Theoretical Probability

ID: A

21

343 ANS:

2x − 7

2= (5 − x)2

2x − 7 = 25− 10x + x2

0 = x2 − 12x + 32

0 = (x − 8)(x − 4)

x = 4,8

2(4) − 7 + 4 = 5

1 = 1

2(8) − 7 + 8 = 5

9 ≠ −3


344 ANS: 3Since x + 4 is a factor of p(x), there is no remainder.

PTS: 2 REF: 081621aii NAT: A.APR.B.2 TOP: Remainder Theorem 345 ANS: 2 PTS: 2 REF: 061724aii NAT: A.SSE.B.4

TOP: Series 346 ANS:

x = y − 3

3+ 1

x − 1 = y − 3

3

x − 13 = y − 3

x − 13 + 3 = y

f −1 (x) = x − 13 + 3

PTS: 2 REF: fall1509aii NAT: F.BF.B.4 TOP: Inverse of FunctionsKEY: other

347 ANS: 12 1 0 -4 -4 8

2 4 0 -81 2 0 -4 0

Since there is no remainder when the quartic is divided by x − 2, this binomial is a factor.

PTS: 2 REF: 061711aii NAT: A.APR.B.2 TOP: Remainder Theorem 348 ANS: 3 PTS: 2 REF: 061623aii NAT: F.BF.A.2

TOP: Sequences

ID: A

22

349 ANS: 2

x = −34 y + 2

−4x = 3y − 8

−4x + 8 = 3y

−43 x + 8

3 = y


350 ANS:

x53

65

= y56

65

x2 = y


351 ANS: No, because P(M / R) ≠ P(M)

70180 ≠ 230

490

0.38 ≠ 0.47


Bar Harbor PhoenixMinimum 31.386 66.491Midline 55.3 86.729Maximum 79.214 106.967Range 47.828 40.476


ID: A

23

353 ANS: 4% 8.75 = 1.25(1 + r)49

7 = (1+ r)49

r + 1 = 749

r ≈.04

or 8.75 = 1.25e 49r

ln7 = lne 49r

ln7 = 49r

r = ln749

r ≈.04

PTS: 2 REF: 081730aii NAT: F.LE.A.4 TOP: Exponential Growth 354 ANS:

69


355 ANS: 4

The vertex is (1,0) and p = 2. y = 14(2) (x − 1)2 + 0


f(7) − f(−7)7− −7 =

= 2−0.25(7) • sin π2 (7)

− 2−0.25(−7) • sin π2 (−7)

14 ≈ −0.26


(1) B(60) −B(10)

60 − 10 ≈ 28% (2) B(69) −B(19)

69 − 19 ≈ 33% (3) B(72) −B(36)

72 − 36 ≈ 38% (4) B(73) −B(60)

73 − 60 ≈ 46%

PTS: 2 REF: 011721aii NAT: F.IF.B.6 TOP: Rate of Change 358 ANS: 1 PTS: 2 REF: 011704aii NAT: F.TF.C.8

TOP: Simplifying Trigonometric Expressions

ID: A

24

359 ANS: 3p

p − 5 =p + 2p + 3

3p 2 + 9p = p 2 − 3p − 10

2p 2 + 12p + 10 = 0

p 2 + 6p + 5 = 0

(p + 5)(p + 1) = 0

p = −5,−1


360 ANS: x2 (4x − 1) + 4(4x − 1) = (x2 + 4)(4x − 1)


361 ANS: 3(m− 2)2(m+ 3) = (m2 − 4m+ 4)(m+ 3) = m3 + 3m2 − 4m2 − 12m+ 4m+ 12 = m3 −m2 − 8m+ 12


362 ANS:

P(W / D) =P(W^D)

P(D) = .4.5 =.8

PTS: 2 REF: 081726aii NAT: S.CP.B.6 TOP: Conditional Probability 363 ANS:

6.25 − 2.2521− 5 = 4

16 = $.25 fine per day. 2.25− 5(.25) = $1 replacement fee. an = 1.25 + (n − 1)(.25). a 60 = $16

PTS: 4 REF: 081734aii NAT: F.BF.A.2 TOP: Sequences 364 ANS: 4 PTS: 2 REF: 012014aii NAT: S.IC.B.5

TOP: Analysis of Data

ID: A

25

365 ANS:

0 = t − 2t + 6

2t − 6 = t

4t2 − 24t + 36 = t

4t2 − 25t + 36 = 0

(4t − 9)(t − 4) = 0

t = 94 ,4

2 94

− 6 < 0, so 94 is extraneous.

( 1 − 2(1) + 6) − ( 3 − 2(3) + 6) = 5− 3 ≈ 3.268 327 mph

PTS: 6 REF: 011737aii NAT: A.REI.A.2 TOP: Solving RadicalsKEY: context

366 ANS: 2

m53

−12

= m−

56 = 1

m56


367 ANS:

x − 5 2x 3 − 4x2 − 7x − 10

2x3 − 10x2

6x2 − 7x

6x2 − 30x

23x − 10

23x − 115

105

2x2 + 6x + 23 Since there is a remainder, x − 5 is not a factor.

PTS: 2 REF: 061627aii NAT: A.APR.B.2 TOP: Remainder Theorem

ID: A

26

368 ANS: 3

log0.8V

17000

= t

0.8t = V17000

V = 17000(0.8) t

17,000(0.8)3 − 17,000(0.8)1

3− 1 ≈ −2450


k 4 − 4k 2 + 8k 3 − 32k + 12k 2 − 48

k 2 (k 2 − 4) + 8k(k 2 − 4) + 12(k 2 − 4)

(k 2 − 4)(k 2 + 8k + 12)

(k + 2)(k − 2)(k + 6)(k + 2)

PTS: 2 REF: fall1505aii NAT: A.SSE.A.2 TOP: Factoring PolynomialsKEY: factoring by grouping

370 ANS:

As x → −3, y → −∞ . As x → ∞, y → ∞ .


H(t) is at a minimum at 70(−1) + 80 = 10


372 ANS:

x3 • x = x13 • x

12 = x

36 • x

36 = x

56


ID: A

27

373 ANS: 0 = 6(−5)3 + b(−5)2 − 52(−5) + 15

0 = −750+ 25b + 260+ 15

475 = 25b

19 = b

z x = 6x3 + 19x 2 − 52x + 15

-5 6 19 -52 15

-30 55 15

6 -11 3 0

6x2 − 11x + 3 = 0

(2x − 3)(3x − 1) = 0

x = 32 , 1

3 ,−5

PTS: 4 REF: fall1515aii NAT: A.APR.B.2 TOP: Remainder Theorem 374 ANS: 2

PTS: 2 REF: 061705aii NAT: A.REI.D.11 TOP: Other Systems 375 ANS: 3 PTS: 2 REF: 012005aii NAT: F.IF.B.4

TOP: Graphing Polynomial Functions 376 ANS:

(4 − 3i)(5+ 2yi − 5 + 2yi)

(4− 3i)(4yi)

16yi − 12yi2

12y + 16yi

PTS: 2 REF: spr1506aii NAT: N.CN.A.2 TOP: Operations with Complex Numbers 377 ANS:

Applying the commutative property, 315

2

can be rewritten as 32

15 or 9

15 . A fractional exponent can be

rewritten as a radical with the denominator as the index, or 915 = 95 .

PTS: 2 REF: 081626aii NAT: N.RN.A.1 TOP: Radicals and Rational Exponents

ID: A

28

378 ANS: 2The events are independent because P(A and B) = P(A) ⋅P(B)

0.125 = 0.5 ⋅ 0.25

.

If P(A or B) = P(A) +P(B) − P(A and B) = 0.25 + 0.5 −.125 = 0.625, then the events are not mutually exclusive because P(A or B) = P(A) + P(B)

0.625 ≠ 0.5 + 0.25

PTS: 2 REF: 061714aii NAT: S.CP.B.7 TOP: Theoretical Probability 379 ANS: 3

x + 2 2x2 + 5x + 82x + 1

2x2 + 4x

x + 8

x + 2

6


380 ANS: 3 PTS: 2 REF: 011710aii NAT: F.BF.A.1TOP: Operations with Functions

381 ANS: 2x(30− 0.01x) − (0.15x3 + 0.01x2 + 2x + 120) = 30x − 0.01x2 − 0.15x3 − 0.01x 2 − 2x − 120

= −0.15x 3 − 0.02x 2 + 28x − 120

PTS: 2 REF: 061709aii NAT: F.BF.A.1 TOP: Operations with Functions 382 ANS:

j(−x) = (−x)4 − 3(−x)2 − 4 = x 2 − 3x 2 − 4 Since j(x) = j(−x), the function is even.

PTS: 2 REF: 081731aii NAT: F.BF.B.3 TOP: Even and Odd Functions 383 ANS: 3

0.75110 ≈.9716


P(A∪B) = P(A) + P(B) −P(A∩B)

0.8 = 0.6+ 0.5 − P(A∩B)

P(A∩B) = 0.3

A and B are independent since P(A∩B) = P(A) ⋅P(B)

0.3 = 0.6 ⋅ 0.5

0.3 = 0.3

PTS: 2 REF: 081632aii NAT: S.CP.A.2 TOP: Probability of Compound EventsKEY: independence

ID: A

29

385 ANS: Jillian’s plan, because distance increases by one mile each week. a 1 = 10

an = an − 1 + 1

an = n + 12


386 ANS: 4 PTS: 2 REF: 061716aii NAT: N.RN.A.2TOP: Radicals and Rational Exponents KEY: variables

387 ANS: 1(x + 3)2 + (2x − 4)2 = 8

x2 + 6x + 9 + 4x2 − 16x + 16 = 8

5x 2 − 10x + 17 = 0

b 2 − 4ac

100− 4(5)(17) < 0


Yes. The margin of error from this simulation indicates that 95% of the observations fall within ± 0.12 of the simulated proportion, 0.25. The margin of error can be estimated by multiplying the standard deviation, shown to

be 0.06 in the dotplot, by 2, or applying the estimated standard error formula, p(1 − p)

n

or

(0.25)(0.75)50

and multiplying by 2. The interval 0.25 ± 0.12 includes plausible values for the true proportion of people who prefer Stephen’s new product. The company has evidence that the population proportion could be at least 25%. As seen in the dotplot, it can be expected to obtain a sample proportion of 0.18 (9 out of 50) or less several times, even when the population proportion is 0.25, due to sampling variability. Given this information, the results of the survey do not provide enough evidence to suggest that the true proportion is not at least 0.25, so the development of the product should continue at this time.

PTS: 4 REF: spr1512aii NAT: S.IC.B.4 TOP: Analysis of Data 389 ANS: 3 PTS: 2 REF: 012015aii NAT: S.IC.B.3

TOP: Analysis of Data KEY: type 390 ANS: 1

8(2x + 3 ) = 48

2x + 3 = 6

(x + 3) ln2 = ln6

x + 3 = ln6ln2

x = ln6ln2 − 3


ID: A

30

391 ANS: 4

x =8 ± (−8)2 − 4(6)(29)

2(6) =8± −632

12 =8 ± i 4 158

12 = 23 ± 1

6 i 158


392 ANS: 4If 1− i is one solution, the other is 1+ i. (x − (1− i))(x − (1 + i)) = 0

x2 − x − ix − x + ix + (1− i2 ) = 0

x 2 − 2x + 2 = 0

PTS: 2 REF: 081601aii NAT: A.REI.B.4 TOP: Complex Conjugate Root Theorem 393 ANS: 3 PTS: 2 REF: 011706aii NAT: S.IC.B.3

TOP: Analysis of Data KEY: type 394 ANS:

period is 23. The wheel rotates once every 2

3 second.


395 ANS:

Based on these data, the two events do not appear to be independent. P(F) = 106200 = 0.53, while

P(F | T) = 5490 = 0.6, P(F | R) = 25

65 = 0.39, and P(F | C) = 2745 = 0.6. The probability of being female are not the

same as the conditional probabilities. This suggests that the events are not independent.

PTS: 2 REF: fall1508aii NAT: S.CP.A.4 TOP: Conditional Probability 396 ANS: 2

h(x) does not have a y-intercept.

PTS: 2 REF: 011719aii NAT: F.IF.C.9 TOP: Comparing Functions 397 ANS: 1 PTS: 2 REF: 081722aii NAT: S.IC.B.6

TOP: Analysis of Data 398 ANS: 3 PTS: 2 REF: 061710aii NAT: S.IC.A.2

TOP: Analysis of Data 399 ANS: 2 PTS: 2 REF: 011720aii NAT: A.APR.B.2

TOP: Remainder Theorem 400 ANS: 1

(1) 9− 02− 1 = 9 (2) 17− 0

3.5 − 1 = 6.8 (3) 0− 05− 1 = 0 (4) 17 − −5

3.5− 1 ≈ 6.3

PTS: 2 REF: 011724aii NAT: F.IF.B.6 TOP: Rate of Change

ID: A

31

401 ANS: 3x2 + 2x + 1 = −5+ 1

(x + 1)2 = −4

x + 1 = ±2i

x = −1± 2i

PTS: 2 REF: 081703aii NAT: A.REI.B.4 TOP: Solving QuadraticsKEY: complex solutions | completing the square

402 ANS: 26xi3 (−4xi + 5) = −24x 2 i4 + 30xi3 = −24x 2 (1) + 30x(−1) = −24x 2 − 30xi


B(t) = 750 1.16112

12t

≈ 750(1.012)12t B(t) = 750 1 + 0.1612

12t

is wrong, because the growth is an annual rate

that is not compounded monthly.

PTS: 2 REF: spr1504aii NAT: A.SSE.B.3 TOP: Modeling Exponential Functions 404 ANS: 3

12

173.83

≈ 0.990656

PTS: 2 REF: 081710aii NAT: A.SSE.B.3 TOP: Modeling Exponential Functions 405 ANS: 3 PTS: 2 REF: 061602aii NAT: A.CED.A.1


Since there are six flavors, each flavor can be assigned a number, 1-6. Use the simulation to see the number of times the same number is rolled 4 times in a row.


The probability of rain equals the probability of rain, given that Sean pitches.


Rewrite 43 as 1

3 ⋅ 41, using the power of a power rule.

PTS: 2 REF: 081725aii NAT: N.RN.A.1 TOP: Radicals and Rational Exponents 409 ANS: 4

The scenario represents a decreasing geometric sequence with a common ratio of 0.80.

PTS: 2 REF: 061610aii NAT: F.BF.A.2 TOP: Sequences

ID: A

32

410 ANS: 3−33t2 + 360t = 700+ 5t

−33t2 + 355t − 700 = 0

t =−355 ± 3552 − 4(−33)(−700)

2(−33) ≈ 3,8

PTS: 2 REF: 081606aii NAT: A.REI.D.11 TOP: Quadratic-Linear Systems 411 ANS: 4

1) −1 is also a zero. 2) x 2 (x − a) + 16(x − a) = (x2 + 16)(x − a) a is the only zero. 3) −a is the only zero. 4) x2 (x − a) − 9(x − a) = (x2 − 9)(x − a).

PTS: 2 REF: 012019aii NAT: A.APR.B.3 TOP: Solving Polynomial Equations 412 ANS:

Translation 3 units right and 4 units up


PTS: 2 REF: 011729aii NAT: F.IF.C.7 TOP: Graphing Polynomial Functions 414 ANS: 2 PTS: 2 REF: 011701aii NAT: F.IF.B.4

TOP: Graphing Trigonometric Functions 415 ANS:

m(3) = 33 − 32 − 5(3) − 3 = 27 − 9 − 15 − 3 = 0 Since m(3) = 0, there is no remainder when m(x) is divided by x − 3, and so x − 3 is a factor.

PTS: 2 REF: 012026aii NAT: A.APR.B.2 TOP: Remainder Theorem 416 ANS: 4 PTS: 2 REF: 012008aii NAT: S.CP.A.3

TOP: Conditional Probability 417 ANS: 1 PTS: 2 REF: 081609aii NAT: F.BF.B.6

TOP: Sigma Notation KEY: represent

ID: A

33

418 ANS: 2The vertex of the parabola is (0,0). The distance, p, between the vertex and the focus or the vertex and the

directrix is 1. y = −14p (x − h)2 + k

y = −14(1) (x − 0)2 + 0

y = −14 x2


PTS: 2 REF: 081604aii NAT: S.ID.A.4 TOP: Normal DistributionsKEY: probability

420 ANS: 1

2x − 1 4x 3 + 0x 2 + 9x − 52x 2 + x + 5

4x 3 − 2x 2

2x 2 + 9x

2x 2 − x

10x − 5

10x − 5


ID: A

34

421 ANS: A = Pert

135000 = 100000e 5r

1.35 = e5r

ln1.35 = lne5r

ln1.35 = 5r

.06 ≈ r or 6%


d = 18; r = ±54

PTS: 2 REF: 011714aii NAT: F.IF.A.3 TOP: SequencesKEY: explicit

423 ANS: 1− i 1− i 1 − i = (1 − 2i + i2 ) 1 − i = −2i 1 − i = −2i + 2i2 = −2 − 2i



425 ANS: 32d(d 3 + 3d 2 − 9d − 27)

2d(d 2 (d + 3) − 9(d + 3))

2d(d 2 − 9)(d + 3)

2d(d + 3)(d − 3)(d + 3)

2d(d + 3)2(d − 3)


ID: A

35

426 ANS: 4

A parabola with a focus of (0,4) and a directrix of y = 2 is sketched as follows: By inspection, it is determined that the vertex of the parabola is (0,3). It is also evident that the distance, p, between the vertex and the focus is 1. It is possible to use the formula (x − h)2 = 4p(y − k) to derive the equation of the parabola as follows: (x − 0)2 = 4(1)(y − 3)

x 2 = 4y − 12

x2 + 12 = 4y

x 2

4 + 3 = y

or A point (x,y) on the parabola must be the same distance from the focus as it is from the directrix. For any such

point (x,y), the distance to the focus is (x − 0)2 + (y − 4)2 and the distance to the directrix is y − 2. Setting this equal leads to: x2 + y2 − 8y + 16 = y 2 − 4y + 4

x2 + 16 = 4y + 4

x 2

4 + 3 = y

PTS: 2 REF: spr1502aii NAT: G.GPE.A.2 TOP: Graphing Quadratic Functions 427 ANS:

x − 2 3x 2 + 7x − 20

3x2 − 6x

13x − 20

13x − 26

6

3x + 13 3x + 13+ 6

x − 2


428 ANS: 3 PTS: 2 REF: 061607aii NAT: S.IC.A.2TOP: Analysis of Data

ID: A

36

429 ANS: 4

log2t = log 10

t log2 = log 10

t =log 10

log2

2) log 10

log2 = log2 10, 1) log2 10 = log2 1012 = 1

2 log210, 3) log410 =log2 10log2 4 = 1

2 log210


430 ANS: 4


The graph shows three real zeros, and has end behavior matching the given end behavior.

PTS: 2 REF: 061604aii NAT: F.IF.C.7 TOP: Graphing Polynomial FunctionsKEY: bimodalgraph

432 ANS:

x83

x43

= x y

x43 = x y

43 = y

PTS: 2 REF: spr1505aii NAT: N.RN.A.2 TOP: Radicals and Rational ExponentsKEY: numbers


ID: A

37

434 ANS: 11) let y = x + 2, then y2 + 2y − 8

(y + 4)(y − 2)

(x + 2+ 4)(x + 2− 2)

(x + 6)x

PTS: 2 REF: 081715aii NAT: A.SSE.A.2 TOP: Factoring PolynomialsKEY: multivariable

435 ANS: 1

P(28) = 5(2)9828 ≈ 56

PTS: 2 REF: 011702aii NAT: F.LE.A.2 TOP: Modeling Exponential Functions 436 ANS:

y = 4.168(3.981)x . 100 = 4.168(3.981)x

log 1004.168 = log(3.981)x

log 1004.168 = x log(3.981)

log 1004.168

log(3.981) = x

x ≈ 2.25


437 ANS: 1157

25 + 47 + 157


(x2 + y2 )2 = (x2 − y2 )2 + (2xy)2

x4 + 2x2y2 + y4 = x4 − 2x2y2 + y4 + 4x2y 2

x4 + 2x2y2 + y4 = x4 + 2x2y2 + y4

PTS: 2 REF: 081727aii NAT: A.APR.C.4 TOP: Polynomial Identities

ID: A

38

439 ANS: 0 = log10 (x − 4)

100 = x − 4

1 = x − 4

x = 5

The x-intercept of h is (2,0). f has the larger value.

PTS: 2 REF: 081630aii NAT: F.IF.C.9 TOP: Comparing Functions 440 ANS:

ln 12

1590 is negative, so M(t) represents decay.


Amplitude, because the height of the graph shows the volume of the air.

PTS: 2 REF: 081625aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: mixed

442 ANS: 2x + 14 = 2x + 5 + 1

x + 14 = 2x + 5+ 2 2x + 5 + 1

−x + 8 = 2 2x + 5

x2 − 16x + 64 = 8x + 20

x2 − 24x + 44 = 0

(x − 22)(x − 2) = 0

x = 2,22

22+ 14 − 2(22) + 5 = 1

6− 7 ≠ 1

PTS: 2 REF: 081704aii NAT: A.REI.A.2 TOP: Solving RadicalsKEY: advanced

ID: A

39

443 ANS:

PTS: 2 REF: 061729aii NAT: F.IF.C.7 TOP: Graphing Exponential Functions 444 ANS: 4

496± 2(115)

PTS: 2 REF: 011718aii NAT: S.ID.A.4 TOP: Normal DistributionsKEY: interval

445 ANS:

At 1.95 years, the value of the car equals the loan balance. Zach can cancel the policy after 6 years.


2x3 − 10x2 + 11x − 7 = 2x3 + hx 2 + 3x − 8x2 − 4hx − 12+ k

−2x2 + 8x + 5 = hx 2 − 4hx + k

h = −2

k = 5


(3k − 2i)2 = 9k 2 − 12ki + 4i2 = 9k 2 − 12ki − 4


ID: A

40

448 ANS: 4y = g(x) = (x − 2)2 (x − 2)2 = 3x − 2

x 2 − 4x + 4 = 3x − 2

x2 − 7x + 6 = 0

(x − 6)(x − 1) = 0

x = 6,1

y = 3(6) − 2 = 16

y = 3(1) − 2 = 1

PTS: 2 REF: 011705aii NAT: A.REI.C.7 TOP: Quadratic-Linear Systems 449 ANS: 4 PTS: 2 REF: 012016aii NAT: F.IF.B.4

TOP: Graphing Trigonometric Functions KEY: increasing/decreasing 450 ANS: 2

cosθ = ± 1 −− 2

5

2

= ± 2525 − 2

25 = ±235

PTS: 2 REF: 061712aii NAT: F.TF.C.8 TOP: Determining Trigonometric Functions 451 ANS: 1

x + y + z = 9

x − y − z = −1

2x = 8

x = 4

4 − y − z = −1

4 − y + z = 21

−y − z = −5

−y + z = 17

−2y = 12

y = −6

4 − 6 + z = 9

z = 11


452 ANS: 4−3x2 − 5x + 2

x3 + 2x2 =(−3x + 1)(x + 2)

x2(x + 2)= −3x

x2 + 1x2 = −3x−1 + x−2

PTS: 2 REF: 061723aii NAT: A.APR.D.6 TOP: Expressions with Negative ExponentsKEY: variables

ID: A

41

453 ANS:

Part a sketch is shifted π3 units right.


454 ANS:

A = 5000(1.045)n

B = 5000 1 + .0464

4n

5000 1 + .0464

4(6)

− 5000(1.045)6 ≈ 6578.87− 6511.30 ≈ 67.57 10000 = 5000 1 + .0464

4n

2 = 1.01154n

log2 = 4n ⋅ log1.0115

n =log2

4log1.0115

n ≈ 15.2

PTS: 6 REF: 081637aii NAT: A.CED.A.1 TOP: Exponential Growth 455 ANS: 2 PTS: 2 REF: 011709aii NAT: S.IC.B.5

TOP: Analysis of Data 456 ANS: 4

d = 32(.8)b − 1 Sn =32 − 32(.8)12

1 −.8 ≈ 149


ID: A

42

457 ANS:

−2x + 1 = −2x2 + 3x + 1

2x 2 − 5x = 0

x(2x − 5) = 0

x = 0, 52

PTS: 2 REF: fall1507aii NAT: A.REI.C.7 TOP: Quadratic-Linear Systems 458 ANS: 3 PTS: 2 REF: 081705aii NAT: F.IF.B.4

TOP: Graphing Trigonometric Functions KEY: increasing/decreasing 459 ANS: 1

x4 − 4x 3 − 9x 2 + 36x = 0

x 3 (x − 4) − 9x(x − 4) = 0

(x3 − 9x)(x − 4) = 0

x(x2 − 9)(x − 4) = 0

x(x + 3)(x − 3)(x − 4) = 0

x = 0,±3,4

PTS: 2 REF: 061606aii NAT: A.APR.B.3 TOP: Solving Polynomial Equations

ID: A

43

460 ANS:

The amplitude, 12, can be interpreted from the situation, since the water level has a minimum of −12 and a maximum of 12. The value of A is −12 since at 8:30 it is low tide. The period of the function is 13 hours, and is expressed in the function through the parameter B. By experimentation with

technology or using the relation P = 2πB (where P is the period), it is determined that B = 2π

13 .

f(t) = −12cos 2π13 t

In order to answer the question about when to fish, the student must interpret the function and determine which choice, 7:30 pm or 10:30 pm, is on an increasing interval. Since the function is increasing from t = 13 to t = 19.5 (which corresponds to 9:30 pm to 4:00 am), 10:30 is the appropriate choice.

PTS: 6 REF: spr1514aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: graph

461 ANS:

PTS: 2 REF: 012032aii NAT: F.IF.C.7 TOP: Graphing Polynomial Functions 462 ANS:

normcdf(510, 540, 480, 24) = 0.0994 z = 510− 48024 = 1.25

z = 540− 48024 = 2.5

1.25 = x − 51020

x = 535

2.5 = x − 51020

x = 560

535-560

PTS: 4 REF: fall1516aii NAT: S.ID.A.4 TOP: Normal DistributionsKEY: probability

ID: A

44

463 ANS: x − 4 = −x + 6

x − 4 = x2 − 12x + 36

0 = x2 − 13x + 40

0 = (x − 8)(x − 5)

x = 5, 8

x − 4 = −8 + 6 = −2 is extraneous.


464 ANS: f(4) − f(−2)

4− −2 = 80 − 1.256 = 13.125

g(4) − g(−2)4− −2 = 179 − −49

6 = 38

g(x) has a greater rate of change

PTS: 4 REF: 061636aii NAT: F.IF.C.9 TOP: Comparing Functions 465 ANS: 4

(x + y)3 = x 3 + 3x2 y + 3xy2 + y3 ≠ x 3 + 3xy + y3


Combining (1) and (3): −6c = −18

c = 3

Combining (1) and (2): 5a + 3c = −1

5a + 3(3) = −1

5a = −10

a = −2

Using (3): −(−2) − 5b − 5(3) = 2

2 − 5b − 15 = 2

b = −3


467 ANS: 1

81x8 y64 = 8114 x

84 y

64 = 3x 2 y

32


ID: A

45

468 ANS: 3(x + a)2 + 5(x + a) + 4 let u = x + a

u 2 + 5u + 4

(u + 4)(u + 1)

(x + a + 4)(x + a + 1)

PTS: 2 REF: 012006aii NAT: A.SSE.A.2 TOP: Factoring PolynomialsKEY: multivariable

469 ANS: Let x equal the first integer and x + 1 equal the next. (x + 1)2 − x 2 = x2 + 2x + 1− x 2 = 2x + 1. 2x + 1 is an odd integer.

PTS: 2 REF: fall1511aii NAT: A.APR.C.4 TOP: Polynomial Identities 470 ANS: 1

PTS: 2 REF: 061617aii NAT: F.TF.A.2 TOP: Determining Trigonometric FunctionsKEY: extension to reals

471 ANS: 4 PTS: 2 REF: 081622aii NAT: F.BF.A.1TOP: Modeling Exponential Functions

472 ANS: 4

As the range is [4,10], the midline is y = 4+ 102 = 7.

PTS: 2 REF: fall1506aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: mixed

473 ANS: 2-4 1 -11 16 84

-4 60 -3041 -15 76

Since there is a remainder when the cubic is divided by x + 4, this binomial is not a factor.

PTS: 2 REF: 081720aii NAT: A.APR.B.2 TOP: Remainder Theorem

ID: A

46

474 ANS: 3(3) repeats 3 times over 2π .

PTS: 2 REF: 011722aii NAT: F.IF.C.7 TOP: Graphing Trigonometric FunctionsKEY: recognize | bimodalgraph

475 ANS: 3 PTS: 2 REF: 081724aii NAT: F.BF.A.2TOP: Sequences

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JMAP REGENTS AT RANDOM - Free resources for Algebra I ......Algebra II Regents Exam Questions at Random 3 10 Written in simplest form, the fraction x3 −9x 9−x2, where x ≠±3,